]>
2018
11
1
ISSN 2008-1898
170
An existence theorem on Hamiltonian \((g,f)\)-factors in networks
An existence theorem on Hamiltonian \((g,f)\)-factors in networks
en
en
Let \(a,b\), and \(r\) be nonnegative integers with
\(\max\{3,r+1\}\leq a<b-r\), let \(G\) be a graph of order \(n\), and let \(g\) and
\(f\) be two integer-valued functions defined on \(V(G)\) with
\(\max\{3,r+1\}\leq a\leq g(x)<f(x)-r\leq b-r\) for any \(x\in V(G)\).
In this article, it is proved that if
\(n\geq\frac{(a+b-3)(a+b-5)+1}{a-1+r}\) and
\({\rm bind}(G)\geq\frac{(a+b-3)(n-1)}{(a-1+r)n-(a+b-3)}\), then \(G\)
admits a Hamiltonian \((g,f)\)-factor.
1
7
Sizhong
Zhou
School of Science
Jiangsu University of Science and Technology
P. R. China
zsz_cumt@163.com
Network
graph
binding number
Article.1.pdf
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]
Lyapunov-type inequalities for Laplacian systems and applications to boundary value problems
Lyapunov-type inequalities for Laplacian systems and applications to boundary value problems
en
en
In this paper, we establish some new
Lyapunov-type inequalities for a class of Laplacian systems.
With these, sufficient conditions for the non-existence of nontrivial solutions to certain
boundary value problems are obtained. A lower bound for the eigenvalues is also deduced.
8
16
Qiao-Luan
Li
College of Mathematics and Information Science
Hebei Normal University, Shijiazhuang
China
qll71125@163.com
Wing-Sum
Cheung
Department of Mathematics
The University of Hong Kong
China
wscheung@hku.hk
Lyapunov type inequality
boundary value problem
Laplacian systems
Article.2.pdf
[
[1]
T. Abdeljawad, A Lyapunov type inequality for fractional operators with nonsingular Mittag-Leffler kernel, J. Inequal. Appl., 2017 (2017), 1-11
##[2]
R. P. Agarwal, A. Özbekler, Lyapunov type inequalities for second order forced mixed nonlinear impulsive differential equations, Appl. Math. Comput., 282 (2016), 216-225
##[3]
M. F. Aktaş, D. Çakmak, A Tiryaki, On the Lyapunov-type inequalities of a three-point boundary value problem for third order linear differential equations, Appl. Math. Lett., 45 (2015), 1-6
##[4]
L.-Y. Chen, C.-J. Zhao, W.-S. Cheung, On Lyapunov-type inequalities for two-dimensional nonlinear partial systems, J. Inequal. Appl., 2010 (2010), 1-12
##[5]
P. L. De Nápoli, J. P. Pinasco, Estimates for eigenvalues of quasilinear elliptic systems, J. Differential Equations, 227 (2006), 102-115
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S. Dhar, Q.-K. Kong, Lyapunov-type inequalities for higher order half-linear differential equations, Appl. Math. Comput., 273 (2016), 114-124
##[7]
M. Jleli, B. Samet, On Lyapunov-type inequalities for (p, q)-Laplacian systems, J. Inequal. Appl., 2017 (2017), 1-9
##[8]
A. Tiryaki, D. Çakmak, M. F. Aktaş, Lyapunov-type inequalities for a certain class of nonlinear systems, Comput. Math. Appl., 64 (2012), 1804-1811
##[9]
X.-P.Wang, Lyapunov type inequalities for second-order half-linear differential equations, J. Math. Anal. Appl., 382 (2011), 792-801
##[10]
Y.-Y. Wang, Y.-N. Li, Y.-Z. Bai, Lyapunov-type inequalities for quasilinear systems with antiperiodic boundary conditions, Russian version appears in Ukraïn. Mat. Zh., 65 (2013), 1646–1656, Ukrainian Math. J., 65 (2014), 1822-1833
##[11]
X.-J. Yang, On inequalities of Lyapunov type, Appl. Math. Comput., 134 (2003), 293-300
]
Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term
Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term
en
en
In this paper, we propose a finite difference method for the Riesz space fractional diffusion equations with delay and a nonlinear source term on a finite domain.
The proposed method combines a time scheme based on the predictor-corrector method and the Crank-Nicolson scheme for the spatial discretization.
The corresponding theoretical results including stability and convergence are provided. Some numerical examples are presented to validate the proposed method.
17
25
Shuiping
Yang
School of Mathematics and Big Data Science
Huizhou University
China
yang52053052@163.com
Riesz fractional derivative
fractional diffusion equations
Crank-Nicolson scheme
stability
convergence
Article.3.pdf
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]
Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces
Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces
en
en
In this paper, we obtain bounded criteria on certain
weighted Morrey spaces for the commutators generalized by some sublinear
integral operators and weighted Lipschitz functions. We also present bounded
criteria for commutators generalized by such sublinear integral operators
and weighted BMO function on the weighted Morrey spaces. As applications, our
results yield the same bounded criteria for those commutators on the
classical weighted Morrey spaces.
26
48
Xiaoli
Chen
Department of Mathematics
Jiangxi Normal University Nanchang
P. R. China
littleli_chen@163.com
Weighted Morrey space
criteria
commutator
weighted Lipschitz function
Article.4.pdf
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]
On some rational systems of difference equations
On some rational systems of difference equations
en
en
Our goal in this paper is to find the form of solutions for the following
systems of rational difference equations:
\[
x_{n+1}=\frac{x_{n-3}y_{n-4}}{y_{n}(\pm 1\pm x_{n-3}y_{n-4})},\quad
y_{n+1}=\frac{y_{n-3}x_{n-4}}{x_{n}(\pm 1\pm y_{n-3}x_{n-4})},\quad n=0,1,\ldots,
\]
where the initial conditions have non-zero real numbers.
49
72
M. M.
El-Dessoky
Mathematics Department, Faculty of Science
Department of Mathematics, Faculty of Science
King AbdulAziz University
Mansoura University
Saudi Arabia
Egypt
dessokym@mans.edu.eg
A.
Khaliq
Department of Mathematics
Riphah International University
Pakistan
khaliqsyed@gmail.com
A.
Asiri
Mathematics Department, Faculty of Science
King AbdulAziz University
Saudi Arabia
amkasiri@kau.edu.sa
Form of solution
stability
rational difference equations
rational systems
Article.5.pdf
[
[1]
E. O. Alzahrani, M. M. El-Dessoky, E. M. Elsayed, Y. Kuang, Solutions and Properties of Some Degenerate Systems of Difference Equations, J. Comput. Anal. Appl., 18 (2015), 321-333
##[2]
H. Bao, On a System of Second-Order Nonlinear Difference Equations, J. Appl. Math. Phys., 3 (2015), 903-910
##[3]
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Q. Din, M. N. Qureshi, A. Q. Khan, Dynamics of a fourth-order system of rational difference equations, Adv. Difference Equ., 2012 (2012 ), 1-15
##[7]
Q. Din, M. N. Qureshi, A. Q. Khan, Qualitative behavior of an anti-competitive system of third-order rational difference equations, Comput. Ecol. Softw., 4 (2014), 104-115
##[8]
M. M. El-Dessoky, On a systems of rational difference equations of Order Two, Proc. Jangjeon Math. Soc., 19 (2016), 271-284
##[9]
M. M. El-Dessoky, Solution of a rational systems of difference equations of order three, Mathematics, 2016 (2016 ), 1-12
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M. M. El-Dessoky, The form of solutions and periodicity for some systems of third -order rational difference equations, Math. Method Appl. Sci., 39 (2016), 1076-1092
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X. Yang, Y. Liu, S. Bai, On the system of high order rational difference equations \(x_{n+1} = \frac{\alpha}{ y_{n-p}}, y_{n+1} = \frac{by_{n-p}}{ x_{n-q}y_{n-p}}\), Appl. Math. Comput., 171 (2005), 853-856
]
Common fixed points of monotone Lipschitzian semigroups in Banach spaces
Common fixed points of monotone Lipschitzian semigroups in Banach spaces
en
en
In this paper, we investigate the existence of common fixed points of monotone Lipschitzian semigroup in Banach spaces under the natural condition that the images under the action of the semigroup at certain point are comparable to the point. In particular, we prove that if one map in the semigroup is a monotone contraction mapping, then such common fixed point exists. In the case of monotone nonexpansive semigroup we prove the existence of common fixed points if the Banach space is uniformly convex in every direction. This assumption is weaker than uniform convexity.
73
79
M.
Bachar
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
mbachar@ksu.edu.sa
Mohamed A.
Khamsi
Department of Mathematical Sciences
Department of Mathematics & Statistics
The University of Texas at El Paso
King Fahd University of Petroleum and Minerals
U. S. A.
Saudi Arabia
mohamed@utep.edu
W. M.
Kozlowski
School of Mathematics and Statistics
University of New South Wales
Australia
w.m.kozlowski@unsw.edu.au
M.
Bounkhel
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bounkhel@ksu.edu.sa
Common fixed point
fixed point
monotone contraction mappings
monotone nonexpansive mappings
monotone Lipschitzian semigroup
Article.6.pdf
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M. R. Alfuraidan, M. A. Khamsi, Fibonacci-Mann iteration for monotone asymptotically nonexpansive mappings, Bull. Aust. Math. Soc., 96 (2017), 307-316
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M. Bachar, M. A. Khamsi, On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces, Fixed Point Theory Appl., 2015 (2015 ), 1-11
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M. Bachar, M. A. Khamsi, Recent contributions to fixed point theory of monotone mappings, J. Fixed Point Theory Appl., 19 (2017), 1953-1976
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]
On the rational difference equation \(y_{{n+1}}={\frac {\alpha_{{0}}y_{{n}}+\alpha_{{1}}y_{{n-p}}+\alpha_{{2}}y_{{n-q}} +\alpha_{{3}}y_{{n-r}}+\alpha_{{4}}y_{{n-s}}}{\beta_{{0}}y_{{n}}+\beta_{{1}}y_{{n-p} }+\beta_{{2}}y_{{n-q}}+\beta_{{3}}y_{{n-r}}+\beta_{{4}}y_{{n-s}}}}\)
On the rational difference equation \(y_{{n+1}}={\frac {\alpha_{{0}}y_{{n}}+\alpha_{{1}}y_{{n-p}}+\alpha_{{2}}y_{{n-q}} +\alpha_{{3}}y_{{n-r}}+\alpha_{{4}}y_{{n-s}}}{\beta_{{0}}y_{{n}}+\beta_{{1}}y_{{n-p} }+\beta_{{2}}y_{{n-q}}+\beta_{{3}}y_{{n-r}}+\beta_{{4}}y_{{n-s}}}}\)
en
en
In this paper, we examine and explore the boundedness, periodicity, and global stability of the positive solutions of
the rational difference equation
\[
y_{{n+1}
}={\frac {\alpha_{{0}}y_{{n}}+\alpha_{{1}}y_{{n-p}}+\alpha_{{2}}y_{{n-q}} +\alpha_{{3}}y_{{
n-r}}+\alpha_{{4}}y_{{n-s}}}{\beta_{{0}}y_{{n}}+\beta_{{1}}y_{{n-p} }+\beta_{{2}}y_{{n-q}
}+\beta_{{3}}y_{{n-r}}+\beta_{{4}}y_{{n-s}}}},
\]
where the coefficients \({\alpha_{i},\beta_{i}\in (0,\infty ),\
i=0,1,2,3,4},\) and \(p,q,r\), and \(s\) are positive integers. The initial
conditions \(y_{-s},...,y_{-r},..., y_{-q},..., y_{{-p }},...,
y_{-1},y_{0}\) are arbitrary positive real numbers such that \(p<q<r<s\).
Some numerical examples will be given to illustrate our result.
80
97
A. M.
Alotaibi
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
ab-alo@hotmail.com
M. A.
El-Moneam
Mathematics Department, Faculty of Science
Jazan University
Kingdom of Saudi Arabia
maliahmedibrahim@jazanu.edu.sa
M. S. M.
Noorani
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
msn@ukm.edu.my
Difference equation
boundedness
prime period two solution
global stability
Article.7.pdf
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E. M. E. Zayed, M. A. EL-Moneam, On the rational recursive sequence \(x_{n+1}=\frac{D+\alpha x_{n}+\beta x_{n-1}+\gamma x_{n-2}}{Ax_{n}+Bx_{n-1}+Cx_{n-2}}\), Comm. Appl. Nonlinear Anal., 12 (2005), 15-28
##[10]
E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence \(x_{n+1}=\frac{\alpha x_{n}+\beta x_{n-1}+\gamma x_{n-2}+\delta x_{n-3}}{Ax_{n}+Bx_{n-1}+Cx_{n-2}+Dx_{n-3}}\) , J. Appl. Math. Comput., 22 (2006), 247-262
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E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence\(x_{n+1}=\left( A+\sum_{i=0}^{k}\alpha _{i}x_{n-i}\right) /\left(B+\sum_{i=0}^{k}\beta _{i}x_{n-i}\right)\), Int. J. Math. Math. Sci., 2007 (2007), 1-12
##[12]
E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence \(x_{n+1}=\left( A+\sum_{i=0}^{k}\alpha _{i}x_{n-i}\right)/\sum_{i=0}^{k}\beta _{i}x_{n-i}\), Math. Bohem., 133 (2008), 225-239
##[13]
E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence \(x_{n+1}=ax_{n}-bx_{n}/\left( cx_{n}-dx_{n-k}\right)\), Comm. Appl. Nonlinear Anal., 15 (2008), 47-57
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E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence \(x_{n+1}=Ax_{n}+\left( \beta x_{n}+\gamma x_{n-k}\right) /\left(Bx_{n}+Cx_{n-k}\right)\), Comm. Appl. Nonlinear Anal., 16 (2009), 91-106
##[15]
E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence \(\ x_{n+1}=\left( \alpha +\beta x_{n-k}\right) /\left( \gamma-x_{n}\right)\), J. Appl. Math. Comput., 31 (2009), 229-237
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E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence \(x_{n+1}=Ax_{n}+Bx_{n-k}+\frac{\beta x_{n}+\gamma x_{n-k}}{ Cx_{n}+Dx_{n-k}}\), Acta. Appl. Math., 111 (2010), 287-301
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E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence \(x_{n+1}=\gamma x_{n-k}+\left( ax_{n}+bx_{n-k}\right) /\left( cx_{n}-dx_{n-k}\right)\), Bull. Iranian Math. Soc., 36 (2010), 103-115
##[19]
E. M. E. Zayed, M. A. El-Moneam, On the rational recursive two sequences \(x_{n+1}=ax_{n-k}+bx_{n-k}/\left(cx_{n}+\delta dx_{n-k}\right)\), Acta. Math. Vietnam., 35 (2010), 355-369
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E. M. E. Zayed, M. A. El-Moneam, On the global asymptotic stability for a rational recursive sequence, Iran. J. Sci. Technol. Trans. A Sci., 35 (2011), 333-339
##[21]
E. M. E. Zayed, M. A. El-Moneam, On the global attractivity of two nonlinear difference equations, Translated from Sovrem. Mat. Prilozh., 70 (2011), J. Math. Sci. (N.Y.), 177 (2011), 487-499
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]
Fixed point theorems for contractions of rational type in complete metric spaces
Fixed point theorems for contractions of rational type in complete metric spaces
en
en
Samet et al. in
[S. Samet, C. Vetro, H. Yazidi, J. Nonlinear Sci. Appl., \({\bf 6}\) (2013), 162--169]
proved some fixed point theorem for
contractions of rational type.
In order to clarify the mathematical structure of
contractions of rational type,
we generalize this theorem in a general setting.
98
107
Tomonari
Suzuki
Department of Basic Sciences, Faculty of Engineering
Kyushu Institute of Technology
Japan
suzuki-t@mns.kyutech.ac.jp
Fixed point
contraction of rational type
complete metric space
Article.8.pdf
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]
Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application
Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application
en
en
The purpose of this paper is to introduce and consider a new
accelerated hybrid shrinking projection method for finding a
common element of the set \(EP \cap F\) in reflexive Banach spaces,
where \(EP\) is the set of all solutions of a generalized equilibrium problem,
and \(F\) is the common fixed point set of finite uniformly closed families of
countable Bregman quasi-Lipschitz mappings.
It is proved that the sequence generated by the accelerated
hybrid shrinking projection iteration, converges strongly to the
point in \(EP \cap F,\) under some conditions. This result is also
applied to find the fixed point of Bregman asymptotically
quasi-nonexpansive mappings.
It is worth mentioning that, there are multiple projection
points from the multiple points in the projection algorithm.
Therefore the new projection method in this paper can accelerate the convergence
speed of iterative sequence. The new results improve and extend
the previously known ones in the literature.
108
130
Jingling
Zhang
Department of Mathematics
Tianjin University
P. R. China
jlzhang09@tju.edu.cn
Ravi P.
Agarwal
Department of Mathematics
Texas A&M University-Kingsville
U. S. A.
Ravi.Agarwal@tamuk.edu
Nan
Jiang
Department of Mathematics
School of Mechanical Engineering
Tianjin University
Tianjin University
P. R. China
P. R. China
nanj@tju.edu.cn
Bregman distance
Bregman quasi-Lipschitz mapping
accelerated hybrid algorithm
Bregman asymptotically quasi-nonexpansive mappings
equilibrium problem
Article.9.pdf
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]
Quadruple random common fixed point results of generalized Lipschitz mappings in cone \(b\)-metric spaces over Banach algebras
Quadruple random common fixed point results of generalized Lipschitz mappings in cone \(b\)-metric spaces over Banach algebras
en
en
In this paper, we introduce the concept of cone \(b\)-metric spaces over Banach algebras and present some quadruple random coincidence points and quadruple random common fixed point theorems for nonlinear operators in such spaces.
131
149
Chayut
Kongban
KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science
King Mongkuts University of Technology Thonburi (KMUTT)
King Mongkuts University of Technology Thonburi (KMUTT)
Thailand
Thailand
chayut_@hotmail.com
Poom
Kumam
KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
Department of Medical Research
KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science
King Mongkuts University of Technology Thonburi (KMUTT)
China Medical University Hospital, China Medical University
King Mongkuts University of Technology Thonburi (KMUTT)
Thailand
Taiwan
Thailand
poom.kum@kmutt.ac.th
Quadruple random fixed point
quadruple common random fixed point
quadruple random coincidence point
cone \(b\)-metric space over Banach algebra
Article.10.pdf
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Optimal inequalities for a Toader-type mean by quadratic and contraharmonic means
Optimal inequalities for a Toader-type mean by quadratic and contraharmonic means
en
en
In this paper, we present the best possible parameters \(\alpha_i, \beta_i\ (i=1,2,3)\) and \(\alpha_4,\beta_4\in(1/2,1)\) such that the double inequalities
\[\alpha_1Q(a,b)+(1-\alpha_1)C(a,b) <T_{Q,C}(a,b)<\beta_1Q(a,b)+(1-\beta_1)C(a,b),\]
\[\qquad\ Q^{\alpha_2}(a,b)C^{1-\alpha_2}(a,b) <T_{Q,C}(a,b)<Q^{\beta_2}(a,b)C^{1-\beta_2}(a,b),\]
\[\frac{Q(a,b)C(a,b)}{\alpha_3Q(a,b)+(1-\alpha_3)C(a,b)} <T_{Q,C}(a,b)<\frac{Q(a,b)C(a,b)}{\beta_3Q(a,b)+(1-\beta_3)C(a,b)},\]
\[C\left(\sqrt{\alpha_4a^2+(1-\alpha_4)b^2},\sqrt{(1-\alpha_4)a^2+\alpha_4b^2}\right) <T_{Q,C}(a,b)<C\left(\sqrt{\beta_4a^2+(1-\beta_4)b^2},\sqrt{(1-\beta_4)a^2+\beta_4b^2}\right)
\]
hold for all \(a, b>0\) with \(a\neq b\), where \(Q(a,b)\), \(C(a,b)\), and \(T(a,b)\) are the quadratic, contraharmonic, and Toader means, respectively, and \(T_{Q,C}(a,b)=T[Q(a,b),C(a,b)]\). As consequences, we provide new bounds for the complete elliptic integral of the second kind.
150
160
Zhengchao
Ji
Center of Mathematical Sciences
Zhejiang University
China
jizhengchao@zju.edu.cn
Qing
Ding
College of Mathematics and Statistics
Hunan University of Finance and Economics
China
dingqing@hufe.edu.cn
Tiehong
Zhao
Department of Mathematics
Hangzhou Normal University
China
tiehong.zhao@hznu.edu.cn
Toader mean
elliptic integral
quadratic mean
contraharmonic mean
Article.11.pdf
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]
The fuzzy \(C\)-delta integral on time scales
The fuzzy \(C\)-delta integral on time scales
en
en
In this paper, we introduce and study the \(C\)-delta integral of interval-valued functions and fuzzy-valued functions on time scales. Also, some basic properties of the fuzzy \(C\)-delta integral are proved. Finally, we give two necessary and sufficient conditions of integrability.
161
171
Xuexiao
You
College of Computer and Information
School of Mathematics and Statistics
Hohai University
Hubei Normal University
P. R. China
P. R. China
youxuexiao@126.com
Dafang
Zhao
School of Mathematics and Statistics
College of Science
Hubei Normal University
Hohai University
P. R. China
P. R. China
dafangzhao@163.com
Jian
Cheng
School of Mathematics and Statistics
Hubei Normal University
P. R. China
jianchenghs@163.com
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Information Science and Engineering
Linyi University
Linyi University
P. R. China
P. R. China
litongx2007@163.com
\(C\)-Delta integral
fuzzy-valued function
time scale
Article.12.pdf
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]