]>
2017
10
12
ISSN 2008-1898
202
Some new integral inequalities for \(n\)-times differentiable convex and concave functions
Some new integral inequalities for \(n\)-times differentiable convex and concave functions
en
en
In this work, by using an integral identity together with both the Holder and the Power-mean integral inequalities we establish several new inequalities for \(n\)-times differentiable convex and concave mappings.
6141
6148
Selahattin
Maden
Department of Mathematics, Faculty of Sciences and Arts
Ordu University
Turkey
maden55@mynet.com
Huriye
Kadakal
Institute of Science
Ordu University
Turkey
huriyekadakal@hotmail.com
Mahir
Kadakal
Department of Mathematics, Faculty of Sciences and Arts
Giresun University
Turkey
mahirkadakal@gmail.com
İmdat
İscan
Department of Mathematics, Faculty of Sciences and Arts
Giresun University
Turkey
imdat.iscan@giresun.edu.tr
Convex function
concave function
Holder integral inequality
power-mean integral inequality
Article.1.pdf
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P. Cerone, S. S. Dragomir, J. Roumeliotis, J. Sunde , A new generalization of the trapezoid formula for n-time differentiable mappings and applications, Demonstratio Math., 33 (2000), 719-736
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S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, Victoria University, Australia (2000)
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İ. İşcan, M. Kunt , Hermite-Hadamard-Fejer type inequalities for harmonically quasi-convex functions via fractional integrals, Kyungpook Math. J., 56 (2016), 845-859
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İ. İşcan, M. Kunt , Hermite-Hadamard-Fejer type inequalities for quasi-geometrically convex functions via fractional integrals, J. Math., 2016 (2016), 1-7
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İ. İşcan, S. Turhan , Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral, Moroccan J. Pure Appl. Anal., 2 (2016), 34-46
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İ. İşcan, S. Turhan, S. Maden, Some Hermite-Hadamard-Fejer type inequalities for Harmonically convex functions via Fractional Integral , New Trends Math. Sci., 4 (2016), 1-10
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W.-D. Jiang, D.-W. Niu, Y. Hua, F. Qi, Generalizations of Hermite-Hadamard inequality to n-time differentiable function which are s-convex in the second sense, Analysis (Munich), 32 (2012), 209-220
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U. S. Kirmaci, M. K. Bakula, M. E. Özdemir, J. Pečarić, Hadamard-type inequalities for s-convex functions, Appl. Math. Comp., 193 (2007), 26-35
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M. E. Özdemir, Ç. Yıldız, New Inequalities for Hermite-Hadamard and Simpson Type with Applications, Tamkang J. Math., 44 (2013), 209-216
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J. E. Pečarić, F. Porschan, Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, Boston (1992)
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S.-H. Wang, B.-Y. Xi, F. Qi , Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich), 32 (2012), 247-262
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B.-Y. Xi, F. Qi , Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means , J. Funct. Spaces Appl., 2012 (2012), 1-14
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Ç. Yıldız, New inequalities of the Hermite-Hadamard type for n-time differentiable functions which are quasiconvex , J. Math. Inequal., 10 (2016), 703-711
]
Wavelet thresholding estimator on \(B_{p,q}^s(\mathbb{R}^n)\)
Wavelet thresholding estimator on \(B_{p,q}^s(\mathbb{R}^n)\)
en
en
This paper deals with the convergence of the wavelet thresholding estimator on Besov spaces \(B_{p,q}^s(\mathbb{R}^n)\). We show firstly the equivalence of several Besov norms. It seems different with one dimensional case. Then we provide two convergence theorems for the wavelet thresholding estimator, which extend Liu and Wang's work [Y.-M. Liu, H.-Y. Wang, Appl. Comput. Harmon. Anal., \({\bf 32}\) (2012), 342--356].
6149
6158
Junjian
Zhao
Department of Mathematics, School of Science
Tianjin Polytechnic University
China
tjzhaojunjian@163.com
Zhitao
Zhuang
School of Mathematics and Information Sciences
North China University of Water Resources and Electric Power
China
zhuangzhitao@emails.bjut.edu.cn
Wavelet thresholding estimator
Besov spaces
convergence
Article.2.pdf
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Y.-M. Liu, H.-Y. Wang, Convergence order of wavelet thresholding estimator for differential operators on Besov spaces, Appl. Comput. Harmon. Anal., 32 (2012), 342-356
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Y.-M. Liu, J.-J. Zhao, An extension of Bittner and Urban’s theorem, Math. Comp., 82 (2013), 401-411
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]
On some extensions of Nadler's fixed point theorem
On some extensions of Nadler's fixed point theorem
en
en
In this paper, we give the notion of the pseudo-fixed point for multi-valued mappings which enable us to extend Nadler's theorem and other well-known results in the literature.
6159
6165
Najeh
Redjel
Laboratory of Informatics and Mathematics
University of Souk-Ahras
Algeria
najehredjel@yahoo.fr
Abdelkader
Dehici
Laboratory of Informatics and Mathematics
University of Souk-Ahras
Algeria
dehicikader@yahoo.fr
Complete metric space
Hausdorff metric
multi-valued mapping
pseudo-fixed point
fixed point
Nadler's fixed point theorem
Article.3.pdf
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J. P. Aubin , Optima and Equilibria: An introduction to Nonlinear Analysis, Springer-Verlag, Berlin (1998)
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Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl., 317 (2006), 103-112
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Inequalities for new class of fractional integral operators
Inequalities for new class of fractional integral operators
en
en
The applications of fractional order integrals have promoted the study of inequalities. In this paper, we utilize recently introduced left- and right-fractional conformable integrals (FCI) for a class of decreasing \(n\) positive functions such that \(n\in N\), for the generalization of existing integral inequalities. Our results have the potentials to be used for the investigation of positive solutions of different classes of fractional differential equations.
6166
6176
Hasib
Khan
College of Engineering, Mechanics and Materials
Department of Mathematics
Hohai University
Shaheed Benazir Bhutto University Sheringal
P. R. China
Pakistan
hasibkhan13@yahoo.com
Hongguang
Sun
College of Engineering, Mechanics and Materials
Hohai University
P. R. China
shg@hhu.edu.cn
Wen
Chen
College of Engineering, Mechanics and Materials
Hohai University
P. R. China
chenwen@hhu.edu.cn
Dumitru
Baleanu
College of Engineering, Mechanics and Materials
Department of Mathematics
Institute of Space Sciences
Hohai University
Cankaya University
P. R. China
Turkey
Romania
dumitru@cankaya.edu.tr
Fractional integral inequalities
left-fractional conformable integral
right-fractional conformable integral
Article.4.pdf
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T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66
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P. Agarwal, M. Jleli, M. Tomar, Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals, J. Inequal. Appl., 2017 (2017), 1-10
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D. Băleanu, R. P. Agarwal, H. Khan, R. A. Khan, H. Jafari , On the existence of solution for fractional differential equations of order \(3 < \delta\leq 4\), Adv. Difference Equ., 2015 (2015), 1-9
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D. Băleanu, H. Khan, H. Jafari, R. A. Khan, M. Alipour, On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions, Adv. Difference Equ., 2015 (2015), 1-14
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D. Băleanu, O. G. Mustafa, On the global existence of solutions to a class of fractional differential equations, Comput. Math. Appl., 59 (2010), 1835-1841
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D. Băleanu, O. G. Mustafa, R. P. Agarwal, On the solution set for a class of sequential fractional differential equations, J. Phys., 2010 (2010), 1-7
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A. Bolandtalat, E. Babolian, H. Jafari, Numerical solutions of multi-order fractional differential equations by Boubaker Polynomials, Open Phys., 14 (2016), 226-230
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A. Debbouche, V. Antonov , Finite-dimensional diffusion models of heat transfer in fractal mediums involving local fractional derivatives, Nonlinear Studies, 24 (2017), 527-535
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H. Jafari, H. K Jassim, S. P. Moshokoa, V. M. Ariyan, F. Tchier , Reduced differential transform method for partial differential equations within local fractional derivative operators, Adv. Mechanical Eng., 2016 (2016), 1-6
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H. Jafari, H. K. Jassim, F. Tchier, D. Baleanu , On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators, Entropy, 2016 (2016), 1-12
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F. Jarad, E. Uğurlu, T. Abdeljawad, D. Baleanu , On a new class of fractional operators, Adv. Difference Equ., 2017 (2017), 1-16
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M. Jleli, M. Kirane, B. Samet , Hartman-Winter-type inequality for a fractional boundary value problem via a fractional derivative with respect to another function, Discrete Dyn Nat Soc., 2017 (2017), 1-8
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H. Khalil, K. Shah, R. A. Khan, Upper and lower solutions to a coupled system of nonlinear fractional differential equations, Progress Frac. Differ. Equ. Appl., 2 (2016), 31-39
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H. Khan, H. Jafari, D. Baleanu, R. A. Khan, A. Khan , On iterative solutions and error estimations of a coupled system of fractional order differential-integral equations with initial and boundary conditions, Differ. Equ. Dyn. Syst., 2017 (2017), 1-13
##[18]
H. Khan, Y. Li, W. Chen, D. Baleanu, A. Khan , Existence of solution and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator , Bound. value Probl., 2017 (2017), 1-16
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A. Khan, Y. Li, K. Shah, T. S. Khan , On coupled p-Laplacian fractional differential equations with nonlinear boundary conditions, Complexity, 2017 (2017), 1-9
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Y. Li, K. Shah, R. A. Khan, Iterative technique for coupled integral boundary value problem of non-linear of non-integer order differential equations, Adv. Difference Equ., 2017 (2017), 1-14
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W. Liu, Q. A. Ngo, V. N. Huy , Several interesting integral inequalities , J. Math. Inequal., 3 (2009), 201-212
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X.-J. Neito, J. A. T. Machado, J. J. Nieto, A new family of the local fractional PDEs , Fund. Inform., 151 (2017), 63-75
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D. O’Regan, B. Samet , Lyapunov-type inequalities for a class of fractional differential equations, J. Inequal. Appl. , 2015 (2015), 1-10
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M. Z. Sarikaya, H. Budak , Generalized Ostrowski type inequalities for local fractional integrals, Proc. Amer. Math. Soc., 145 (2017), 1527-1538
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E. Set, M. A. Noor, M. U. Awan, A. Gözpinar , Generalized Hermite-Hadamard type inequalities involving fractional integral operators, J. Inequal. Appl., 2017 (2017), 1-10
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E. Set, M. Tomar, M. Z. Sarikaya, On fractional Gruss type inequalities for k-fractional integrals, Appl. Math. Comput., 269 (2015), 29-34
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K. Shah, R. A. Khan , Study of solution to a toppled system of fractional Differential Equations with integral boundary conditions , Int. J. Appl. Comput. Math., 3 (2017), 2369-2388
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H.-G. Sun, Y. Zhang, W. Chen, D. M. Reeves, Use of a variable-index fractional-derivative model to capture transient dispersion in heterogeneous media, J. Contaminant Hydrology, 157 (2014), 47-58
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X.-J. Yang, J. A. T. Machao, D. Baleanu, Anomalous diffusion models with general fractional derivatives within the kernels of the extended Mittag-Leffler type functions, Romanian Reports in Physics, 2017 (2017), 1-19
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X.-J. Yang, H. M. Srivastava, J. A. T. Machado, A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow, Therm. Sci., 20 (2016), 753-756
]
Permanence and partial extinction in a delayed three-species food chain model with stage structure and time-varying coefficients
Permanence and partial extinction in a delayed three-species food chain model with stage structure and time-varying coefficients
en
en
By taking full consideration of maturity (\(\tau_{1}\) represents the maturity of predator and \(\tau_{2}\) represents the maturity of top predator)
and the effects of environmental parameters, a new delayed three-species food chain model with stage structure and time-varying coefficients is
established. With the help of the comparison theorem and the technique of mathematical analysis, the positivity and boundedness of solutions of
the model are investigated. Furthermore, some sufficient conditions on the permanence and partial extinction of the system are derived.
Some interesting findings show that the delays have great impacts on the permanence for the system. More precisely, if \(\tau_{2}\in(n, +\infty)\),
then the system is partially extinct: on one hand, if \(\tau_{1}\in(0,n_{1})\) and \(\tau_{2}\in(n, +\infty)\), then the prey and predator species
will coexist, i.e., both the prey and predator species are always permanent, yet the top predator species will go extinct eventually.
On the other hand, if \(\tau_{1}\in(n_{4},+\infty)\) and \(\tau_{2}\in(n, +\infty)\), where \(n_{4}\) is greater than \(n_{1}\),
then all predator species will become extinct eventually. Numerical simulations are great well agreement with the theoretical results.
6177
6191
Huanyan
Xi
Department of Mathematics and Statistics
Changsha University of Science and Technology
P. R. China
huanyanxii@126.com
Lihong
Huang
Department of Mathematics and Statistics
Changsha University of Science and Technology
P. R. China
lhhuang@csust.edu.cn
Yuncheng
Qiao
Department of Mathematics and Statistics
Changsha University of Science and Technology
P. R. China
lyuqyc@163.com
Huaiyu
Li
Department of Mathematics and Statistics
Changsha University of Science and Technology
P. R. China
lee1012116@126.com
Chuangxia
Huang
Department of Mathematics and Statistics
Changsha University of Science and Technology
P. R. China
cxiahuang@126.com
Food chain model
delay
stage structure
permanence
extinction
Article.5.pdf
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Z.-H. Ma, Z.-Z. Li, S.-F. Wang, T. Li, F.-P. Zhang, Permanence of a predator-prey system with stage structure and time delay , Appl. Math. Comput., 201 (2008), 65-71
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W. Mbava, J. Y. T. Mugisha, J. W. Gonsalves, Prey, predator and super-predator model with disease in the super-predator, Appl. Math. Comput., 297 (2017), 92-114
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B. Patra, A. Maiti, G. Samanta, Effect of time-delay on a ratio-dependent food chain model , Nonlinear Anal. Model. Control, 14 (2009), 199-216
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S. Ruan, Y. Tang, W. Zhang, Versal unfoldings of predator-prey systems with ratio-dependent functional response, J. Differential Equations, 249 (2010), 1410-1435
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C. Shen, M. You , Permanence and extinction of a three-species ratio-dependent food chain model with delay and prey diffusion, Appl. Math. Comput., 217 (2010), 1825-1830
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B. Tian, S. Zhong, Z. Liu , Extinction and persistence of a nonautonomous stochastic food-chain system with impulsive perturbations, Int. J. Biomath., 2016 (2016), 1-26
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K.Wang , Permanence and global asymptotical stability of a predator-prey model with mutual interference, Nonlinear Anal. Real World Appl., 12 (2011), 1062-1071
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W. Wang, G. Mulone, F. Salemi, V. Salone, Permanence and stability of a stage-structured predator-prey model, J. Math. Anal. Appl., 262 (2001), 499-528
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R. Xu, M. A. J. Chaplain, F. A. Davidson, Global stability of Lotka-Volterra type predator-prey model with stage structure and time delay, Appl. Math. Comput., 159 (2004), 863-880
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C. Xu, S. Yuan, T. Zhang , Global dynamics of a predator-prey model with defense mechanism for prey, Appl. Math. Lett., 62 (2016), 42-48
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P. Yongzhen, M. Guo, C. Li, A delay digestion process with application in a three-species ecosystem, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 4365-4378
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H. Zhang, L. Chen, R. Zhu, Permanence and extinction of a periodic predator-prey delay system with functional response and stage structure for prey, Appl. Math. Comput., 184 (2007), 931-944
]
Common fixed points for pairs of triangular \(\alpha\)-admissible mappings
Common fixed points for pairs of triangular \(\alpha\)-admissible mappings
en
en
In this paper, we introduce the notation of \((\alpha-\eta)-(\psi-\varphi)\)-contraction mappings defined on a set \(X\).
We prove the existence of common fixed point results for the pair of self-mappings involving C-class functions in the
setting of metric space. Our results generalize and extend several works existing in literature. We provide an example
and some applications in order to support our results.
6192
6204
Haitham
Qawagneh
School of mathematical Sciences, Faculty of Science and Technology
University Kebangsaan Malaysia
Malaysia
haitham.math77@gmail.com
Mohd Salmi
MD Noorani
School of mathematical Sciences, Faculty of Science and Technology
University Kebangsaan Malaysia
Malaysia
msn@ukm.my
Wasfi
Shatanawi
Department of Mathematics and General Courses
Department of Mathematics
Prince Sultan University
Hashemite University
Saudi Arabia
Jordan
wshatanawi@psu.edu.sa;swasfi@hu.edu.jo;wshatanawi@yahoo.com
Habes
Alsamir
Department of Mathematics and General Courses
Aljouf University
Saudi Arabia
h.alsamer@gmail.com
C-class functions
\(\alpha\)-admissible mapping
common fixed point
metric spaces
Article.6.pdf
[
[1]
P. Chuadchawna, A. Kaewcharoen and S. Plubtieng, Fixed point theorems for generalized \(\alpha-\eta-\psi\)-Geraghty contraction type mappings in \(\alpha-\eta-\psi\)-complete metric spaces , J. Nonlinear Sci. Appl., 9 (2016), 471-485
##[2]
S. Alizadeh, F. Moradlou, P. Salimi , Some fixed point results for \((\alpha,\beta) - (\psi,\phi)\)-contractive mappings, Filomat, 28 (2014), 635-647
##[3]
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]
Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting
Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting
en
en
In this paper, we propose a stochastic service-resource mutualism model with Lévy noises and harvesting. Under some assumptions, we study several dynamical properties of the model. We first obtain the thresholds between persistence and extinction for both the service species and the resource species. Then we give sharp sufficient conditions for stability in distribution of the model. Finally, we establish sufficient and necessary criteria for the existence of the optimal harvesting policy. The optimal harvesting effort and maximum of sustainable yield are also obtained. Our results reveal that the persistence, extinction, stability in distribution and optimal harvesting strategy have close relationships with the random noises.
6205
6218
Hui
Wang
School of Mathematical Science
Huaiyin Normal University
P. R. China
Chenxi
Du
School of Mathematical Science
Huaiyin Normal University
P. R. China
Meng
Liu
School of Mathematical Science
School of Mathematics and Statistics
Huaiyin Normal University
Northeast Normal University
P. R. China
P. R. China
liumeng@hytc.edu.cn
Service-resource mutualism model
white noise
Lévy jumps
persistence
optimal harvesting
Article.7.pdf
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E. Braverman, L. Braverman , Optimal harvesting of diffusive models in a nonhomogeneous environment , Nonlinear Anal., 71 (2009), 1-2173
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M. Liu, X. He, J. Yu , Dynamics of a stochastic regime-switching predator-prey model with harvesting and distributed delays, Nonlinear Anal. Hybrid Syst., 28 (2018), 87-104
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]
Identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind arising from nonlinear differential equation
Identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind arising from nonlinear differential equation
en
en
In [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, Glob. J. Pure Appl. Math., \({\bf 12}\) (2016), 1893--1901], Kim et al. presented some identities for the
Bernoulli numbers of the second kind using differential equation.
Here we use this differential equation in a different way. In this
paper, we deduce some identities of the degenerate Daehee numbers
with the Bernoulli numbers of the second kind of order \(r\).
6219
6228
Sung-Soo
Pyo
Department of Mathematics Education
Silla University
Rep. of Korea
ssoopyo@gmail.com
Taekyun
Kim
Department of Mathematics
Kwangwoon University
Rep. of Korea
kwangwoonmath@hanmail.net
Seog-Hoon
Rim
Department of Mathematics Education
Kyungpook National University
Rep. of Korea
shrim@knu.ac.kr
Degenerate Daehee numbers
Bernoulli numbers of the second kind
nonlinear differential equation
Article.8.pdf
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L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers , Utilitas Math., 15 (1979), 51-88
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D. V. Dolgy, T. Kim, L.-C. Jang, H.-I. Kwon, J. J. Seo, Some identities of symmetry for the degenerate q-Bernoulli polynomials under symmetry group of degree n, Glob. J. Pure Appl. Math., 12 (2016), 4385-4394
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B. S. El-Desouky, A. Mustafa, New results on higher-order Daehee and Bernoulli numbers and polynomials, Adv. Difference Equ., 2016 (2016), 1-21
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G.-W. Jang, T. Kim, Revisit of identities of Daehee numbers arising from nonlinear differential equations , Proc. Jangjeon Math. Soc., 20 (2017), 163-177
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G.-W. Jang, T. Kim, Some identities of ordered Bell numbers arising from differential equation, Adv. Stud. Contemp. Math., 27 (2017), 385-397
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G.-W. Jang, J. Kwon, J. G. Lee , Some identities of degenerate Daehee numbers arising from nonlinear differential equation, Adv. Difference Equ., 2017 (2017), 1-10
##[9]
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T. Kim, On the degenerate Cauchy numbers and polynomials, Proc. Jangjeon Math. Soc., 18 (2015), 307-312
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T. Kim, Degenerate Cauchy numbers and polynomials of the second kind, Adv. Stud. Contemp. Math., 27 (2017), 441-449
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D. S. Kim, T. Kim, Some identities for Bernoulli numbers of the second kind arising from a non-linear differential equation, Bull. Korean Math. Soc., 52 (2015), 2001-2010
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T. Kim, D. S. Kim, A note on nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88-92
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D. S. Kim, T. Kim, On degenerate Bell numbers and polynomials, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math., 111 (2017), 435-446
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D. S. Kim, T. Kim, D. V. Dolgy , A note on degenerate Bernoulli numbers and polynomials associated with p-adic invariant integral on \(\mathbb{Z}_p\), Appl. Math. Comput., 259 (2015), 198-204
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D. S. Kim, T. Kim, G. -W. Jang, Some identities of partially degenerate Touchard polynomials arising from differential equations, Adv. Stud. Contemp. Math., 27 (2017), 243-251
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T. Kim, D. S. Kim, K.-W. Hwang, J. J. Seo, Some identities of Laguerre polynomials arising from differential equations , Adv. Difference Equ., 2016 (2016), 1-9
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T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, Higher-order Cauchy Numbers and Polynomials, Appl. Math. Sci., 9 (2015), 1989-2004
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T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, Differential equations arising from the generating function of general modified degenerate Euler numbers, Adv. Difference Equ., 2016 (2016), 1-7
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T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, Revisit nonlinear differential equations associated with Bernoulli numbers of the second kind, Glob. J. Pure Appl. Math., 12 (2016), 1893-1901
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T. Kim, D. S. Kim, T. Mansour, J. J. Seo, Linear differential equations for families of polynomials, J. Inequal. Appl., 2016 (2016), 1-8
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J.-W. Park, J. Kwon, A note on the Degenerate High order Daehee polynomials, Appl. Math. Sic., 9 (2015), 4635-4642
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N. L. Wang, H. Li, Some identities on the Higher-order Daehee and Changhee Numbers , Pure Appl. Math. J., 4 (2015), 33-37
]
Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations
Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations
en
en
This paper focuses on the following elliptic equation
\[
\left\{ \begin{aligned}
-u''- p(x)u=f(x,u),\quad \text{a.e.}\quad x\in[0,l],\\
u(0)-u(l)=u'(0)-u'(l)=0,
\end{aligned} \right. \]
where the primitive function of \(f(x,u)\) is either superquadratic or asymptotically quadratic as \(|u|\rightarrow\infty\), or subquadratic as \(|u|\rightarrow0\). By using variational method, e.g. the local linking theorem, fountain theorem, and the generalized mountain pass theorem, we establish the existence and multiplicity results for the periodic solution and subharmonic solution.
6229
6245
Xiujuan
Wang
School of Mathematical Sciences
Qufu Normal University
P. R. China
1140934106@qq.com
Aixia
Qian
School of Mathematical Sciences
Qufu Normal University
P. R. China
qaixia@amss.ac.cn
Elliptic equation
periodic solution
superquadratic
subquadratic
asymptotically quadratic
subharmonic solution
Article.9.pdf
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M. Schechter, Linking methods in critical point theory, Birkhäuser Boston, Inc., Boston, MA (1999)
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A. J. Ureña, Periodic solutions of singular equations, Topol. Methods Nonlinear Anal., 47 (2016), 55-72
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W.-M. Zou, M. Schechter, Critical point theory and its applications, Springer, New York (2006)
]
An LQP-SQP alternating direction method for solving variational inequality problems with separable structure
An LQP-SQP alternating direction method for solving variational inequality problems with separable structure
en
en
In this paper, by combining the
logarithmic-quadratic proximal (LQP) method and the square
quadratic proximal (SQP) method, we propose an inexact
alternating direction method for solving constrained variational
inequalities \(VI(S,f),\) where \(S\) is a convex set with linear
constraints.
Under certain conditions, the global
convergence of the proposed method is established. We show the
O(1/t) convergence rate for the inexact LQP-SQP alternating
direction method. To demonstrate the efficiency of the proposed
method, we provide numerical results for traffic equilibrium
problems.
6246
6261
Adnan
Alhomaidan
Department of Mathematics
King Abdulaziz University
Saudi Arabia
Abdellah
Bnouhachem
Laboratoire d'Ingénierie des Systèmes et Technologies de l'Information
Ibn Zohr University
Morocco
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Proximal point algorithm
logarithmic-quadratic proximal method
square quadratic proximal
variational inequality
prediction-correction
traffic equilibrium problems
Article.10.pdf
[
[1]
A. E. Al-Mazrooei, A. Latif, J. C. Yao, Solving generalized mixed equilibria, variational inequalities, and constrained convex minimization, Abstr. Appl. Anal., 2014 (2014), 1-26
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A. Auslender, M. Teboulle, S. Ben-Tiba, A logarithmic-quadratic proximal method for variational inequalities, Computational optimization–a tribute to Olvi Mangasarian, Part I, Comput. Optim. Appl., 12 (1999), 31-40
##[3]
A. Bnouhachem, On LQP alternating direction method for solving variational inequality problems with separable structure, J. Inequal. Appl., 2014 (2014), 1-15
##[4]
A. Bnouhachem, Q. H. Ansari , A descent LQP alternating direction method for solving variational inequality problems with separable structure, Appl. Math. Comput., 246 (2014), 519-532
##[5]
A. Bnouhachem, H. Benazza, M. Khalfaoui, An inexact alternating direction method for solving a class of structured variational inequalities , Appl. Math. Comput., 219 (2013), 7837-7846
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A. Bnouhachem, A. Hamdi , Parallel LQP alternating direction method for solving variational inequality problems with separable structure, J. Inequal. Appl., 2014 (2014), 1-14
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A. Bnouhachem, A. Latif, Q. H. Ansari , On the \(O(1/t)\) convergence rate of the alternating direction method with LQP regularization for solving structured variational inequality problems, J. Inequal. Appl., 2016 (2016), 1-14
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A. Bnouhachem, M. H. Xu, An inexact LQP alternating direction method for solving a class of structured variational inequalities, Comput. Math. Appl., 67 (2014), 671-680
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L.-C. Ceng, A. Latif, J.-C. Yao , On solutions of a system of variational inequalities and fixed point problems in Banach spaces, Fixed Point Theory Appl., 2013 (2013), 1-34
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F. Facchinei, J.-S. Pang , Finite-dimensional variational inequalities and complementarity problems, Vol. I and II, Springer Series in Operations Research, Springer-Verlag, New York (2003)
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X.-L. Fu, A. Bnouhachem , An self-adaptive LQP method for constrained variational inequalities, Appl. Math. Comput., 189 (2007), 1586-1600
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H.-J. He, K. Wang, X.-J. Cai, D.-R. Han , An LQP-based two-step method for structured variational inequalities, J. Oper. Res. Soc. China, 5 (2017), 301-317
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B.-S. He, Y. Xu, X.-M. Yuan, A logarithmic-quadratic proximal prediction-correction method for structured monotone variational inequalities, Comput. Optim. Appl., 35 (2006), 19-46
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B.-S. He, J. Zhou, A modified alternating direction method for convex minimization problems , App. Math. Lett., 13 (2000), 123-130
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Z.-K. Jiang, A. Bnouhachem, A projection-based prediction-correction method for structured monotone variational inequalities, Appl. Math. Comput., 202 (2008), 747-759
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S. Kontogiorgis, R. R. Meyer, A variable-penalty alternating directions method for convex optimization , Math. Programming, 83 (1998), 29-53
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A. Latif, D. T. Luc, Variational relation problems: existence of solutions and fixed points of contraction mappings, Fixed Point Theory Appl., 2013 (2013), 1-10
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M. Li , A hybrid LQP-based method for structured variational inequalities, Int. J. Comput. Math., 89 (2012), 1412-1425
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]
Invariance analysis and exact solutions of some sixth-order difference equations
Invariance analysis and exact solutions of some sixth-order difference equations
en
en
We perform a full Lie point symmetry analysis of difference equations of the form
\[
u_{n+6}=\frac{u_nu_{n+4}}{u_{n+2}(A _n + B _n u_nu_{n+4})}\ ,
\]
where the initial conditions are non-zero real numbers. Consequently, we obtain four non-trivial symmetries. Eventually, we get solutions of the difference equation for random sequences \((A_n)\) and \((B_n)\). This work is a generalization of a recent result by Khaliq and Elsayed [A. Khaliq, E. M. Elsayed, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 1052--1063].
6262
6273
Darlison
Nyirenda
School of Mathematics
University of the Witwatersrand
South Africa
Darlison.Nyirenda@wits.ac.za
Mensah
Folly-Gbetoula
School of Mathematics
University of the Witwatersrand
South Africa
Mensah.Folly-Gbetoula@wits.ac.za
Difference equation
symmetry
group invariant solutions
Article.11.pdf
[
[1]
E. M. Elsayed, T. F. Ibrahim, Periodicity and solutions for some systems of nonlinear rational difference equations, Hacet. J. Math. Stat., 44 (2015), 1361-1390
##[2]
G. Feng, X.-J. Yang, H. M. Srivasta, Exact traveling-wave solutions for linear and nonlinear heat-transfer equations, Therm. Sci., 00 (2016), 1-6
##[3]
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]
On the existence of generalized weak solutions to discontinuous fuzzy differential equations
On the existence of generalized weak solutions to discontinuous fuzzy differential equations
en
en
In this paper, by means of replacing the Lebesgue integrability of
support functions with its Henstock integrability, the definitions of the Henstock-Pettis integral of \(n\)-dimensional fuzzy-number-valued
functions are defined. In addition, the controlled convergence theorems for such
integrals are considered. As the applications of these integrals,
we provide some existence theorems of generalized weak solutions to initial value problems for the discontinuous fuzzy differential equations under the strong GH-differentiability.
6274
6287
Ya-Bin
Shao
School of Science
Chongqing University of Posts and Telecommunications
People's Republic of China
yb-shao@163.com
Zeng-Tai
Gong
College of Mathematics and Statistics
Northwest Normal University
People's Republic of China
zt-gong@163.com
Zi-Zhong
Chen
College of Computer Science and Technology
Chongqing University of Posts and Telecommunications
People's Republic of China
chenzz@cqupt.edu.cn
Fuzzy number
fuzzy Henstock-Pettis integral
convergence theorem
discontinuous fuzzy differential equation
generalized weak solution
Article.12.pdf
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]
Periodic problem of first order nonlinear uncertain dynamic systems
Periodic problem of first order nonlinear uncertain dynamic systems
en
en
The solution to fuzzy differential equation
is very important for solving the uncertainly practical problems in the real world.
In this paper, the definition of solution for periodic problems of
fuzzy differential equations based on the theory of differential inclusions is given.
Using the theory of differential inclusions, function analysis and
Kakutani Fixed point theorem, an existence theorem of periodic solutions to first order uncertain
dynamical systems is obtained in a more general set.
6288
6297
Yongzhao
Wang
School of Mathematics and Statistics
Anyang Normal University
China
wangyongzhao1987@126.com
Qian
Liu
School of Civil Engineering and Architecture
Anyang University
China
357050607@qq.com
Qiansheng
Feng
Faculty of Mathematics and Physics
Huaiyin Institute of Technology
China
fengqiansheng-2008@163.com
Fuzzy number
uncertain dynamical system
Kakutani fixed point theorem
differential inclusion
Article.13.pdf
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[1]
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]
A new iterative scheme in CAT(0) spaces with convergence analysis
A new iterative scheme in CAT(0) spaces with convergence analysis
en
en
In this paper, we establish strong and \(\Delta\)-convergence theorems
in CAT\((0)\) spaces for two total asymptotically nonexpansive non-self
mappings via a new two-step iterative scheme for non-self-mappings.
Our results extend and generalize several results from the current
existing literature.
6298
6310
G. S.
Saluja
Department of Mathematics
Govt. Kaktiya P. G. College
India
saluja1963@gmail.com
Adrian
Ghiura
University Politehnica of Bucharest
Romania
adrianghiura25@gmail.com
Mihai
Postolache
China Medical University
University Politehnica of Bucharest
Taiwan
Romania
mihai@mathem.pub.ro
Total asymptotically nonexpansive non-self-mapping
new two-step iterative scheme
common fixed point
strong convergence
\(\Delta\)-convergence
CAT\((0)\) space
Article.14.pdf
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M. Abbas, B. S. Thakur, D. Thakur, Fixed points of asymptotically nonexpansive mappings in the intermediate sense in CAT(0) spaces, Commun. Korean Math. Soc., 28 (2013), 107-121
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G. S. Saluja, Strong and \(\Delta\)-convergence theorems for two totally asymptotically nonexpansive mappings in CAT(0) spaces, Nonlinear Anal. Forum, 20 (2015), 107-120
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G. S. Saluja, Strong convergence theorems for two total asymptotically nonexpansive non-self-mappings in Banach spaces, ROMAI J., 12 (2016), 105-121
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G. S. Saluja, H. K. Nashine, Y. R. Singh, Strong and \(\Delta\)-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Int. J. Nonlinear Anal. Appl., 8 (2017), 245-260
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]
On the mechanism of integration of informatization and industrialization based on dynamics of stochastic model
On the mechanism of integration of informatization and industrialization based on dynamics of stochastic model
en
en
In recent years, with the new generation of information and communication technology in the industrial field more widely used, the integration of informatization and industrialization aroused people's research and attention again. The connotation and mechanism of integration of informatization and industrialization is one of the focuses of people's research. In this paper, a stochastic model that describes the interaction between information and industrial technology is proposed and analyzed. Sharp sufficient conditions for increase and stagnate of the diffusion rates for both information and industrial technology are established. The results reveal that the stochastic perturbations can affect the dynamics of model significantly.
6311
6323
Chaodong
Yan
College of Economics and Management
Nanjing University of Aeronautics and Astronautics
China
yanchaodong@163.com
Jing
Ma
College of Economics and Management
Nanjing University of Aeronautics and Astronautics
China
Dandan
Li
College of Economics and Management
Nanjing University of Aeronautics and Astronautics
China
Integration of the informatization and industrialization
stochastic perturbations
information technology
industrial technology
increase
stagnate
Article.15.pdf
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[1]
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Classifications and duality relations for several integral transforms
Classifications and duality relations for several integral transforms
en
en
In this paper, we classify several integral transforms into two
categories according to the types of their kernel functions and two novel
definitions of general integral transforms are suggested. Based on the general integral transforms, some of their
basic properties are proved. In addition, the dualities between those
two kinds of integral transforms are deducted and discussed in detail. The interesting
coupling relations in symmetric form is illustrated graphically. The
analysis shows that the classifications are reasonable and the dualities are
significant.
6324
6332
Xin
Liang
State Key Laboratory for Geomechanics and Deep Underground Engineering
China University of Mining and Technology
China
xliang@cumt.edu.cn
Feng
Gao
State Key Laboratory for Geomechanics and Deep Underground Engineering
School of Mechanics and Civil Engineering
China University of Mining and Technology
China University of Mining and Technology
China
China
jsppw@sohu.com
Shan-Jie
Su
State Key Laboratory for Geomechanics and Deep Underground Engineering
China University of Mining and Technology
China
ssj_cumt@126.com
Zhen
Wang
College of Mathematics and Systems Science
Shandong University of Science and Technology
China
wangzhen_sd@126.com
Xiao-Jun
Yang
State Key Laboratory for Geomechanics and Deep Underground Engineering
School of Mechanics and Civil Engineering
College of Mathematics and Systems Science
China University of Mining and Technology
China University of Mining and Technology
Shandong University of Science and Technology
China
China
China
dyangxiaojun@163.com
Integral transforms
kernel functions
dualities
Article.16.pdf
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]
Multiple positive solutions of fractional-order boundary value problem with integral boundary conditions
Multiple positive solutions of fractional-order boundary value problem with integral boundary conditions
en
en
We concentrate on investigating the existence of positive solutions
for fractional-order differential equations with integral conditions
in this article. The problem is issued by applying Avery-Peterson
fixed-point theorem and the properties of Green's function. At the
same time, we provide an example to make our results clear and easy
for readers' to understand the multiplicity of solutions.
6333
6343
Youyu
Wang
Department of Mathematics
Tianjin University of Finance and Economics
P. R. China
wang_youyu@163.com
Shuilian
Liang
Department of Mathematics
Tianjin University of Finance and Economics
P. R. China
sunshinelsl@163.com
Qichao
Wang
Department of Mathematics
Tianjin University of Finance and Economics
P. R. China
qichaowang@163.com
Fractional differential equation
integral boundary value conditions
multiplicity of positive solutions
Article.17.pdf
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]
Perfect \(2\)-Colorings of Johnson Graph \(J(10,\,3)\)
Perfect \(2\)-Colorings of Johnson Graph \(J(10,\,3)\)
en
en
A perfect \(2\)-coloring of a graph \(G\) with a matrix \(A=\{a_{ij}\}_{i,j=1,2}\) is a coloring of the vertices of \(G\) into the set of colors \(\{1,2\}\) such that the number of vertices of the color \(j\) adjacent with the fixed vertex \(x\) of the color \(i\) does not depend on a choice of the vertex \(x\) and equals to \(a_{ij}\). The matrix \(A\) is called the parameter matrix of a perfect coloring. We can consider perfect coloring as a generalization of the concept of completely regular codes presented by P. Delsarte for the first time. The parameter matrices of all perfect \(2\)-colorings of the Johnson graph \(J(10,\,3)\) are listed in this paper.
6344
6348
M.
Alaeiyan
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
alaeiyan@iust.ac.ir
A.
Abedi
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
Perfect \(2\)-colorings
Johnson graph \(J(10,\,3)\)
parameter matrices
Article.18.pdf
[
]