]>
2018
11
10
ISSN 2008-1898
101
Dual Orlicz mixed geominimal surface area
Dual Orlicz mixed geominimal surface area
en
en
Based on the classical ideas, Zhu discussed the properties and useful theories for \(L_{p}\)-mixed geominimal surface area; meanwhile, Ma defined dual Orlicz geominimal surface area. The previous studies provide a thought to us for the study of the dual Orlicz mixed geominimal surface. In our paper, we have done the following work: attempting to use an integral form to define the dual Orlicz mixed geominimal surface area, further studyding its related properties, and listing some inequalities including Alexandrov-Fenchel type inequality, analogous cyclic inequality, Blaschke-Santaló type inequality, and affine isoperimetric inequality in Orlicz space.
1113
1123
Li
Gao
College of Mathematics and Statistics
Northwest Normal University
P. R. China
Tongyi
Ma
College of Mathematics and Statistics
Hexi University
P. R. China
matongyi@126.com
Yuanyuan
Guo
College of Mathematics and Statistics
Northwest Normal University
P. R. China
Star bodies
dual Orlicz mixed geominimal surface area
inequality
Article.1.pdf
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C.-J. Zhao, G. S. Leng, Brunn-Minkowski inequality for mixed intersection bodies, J. Math. Anal. Appl., 301 (2005), 115-123
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G. X. Zhu, The Orlicz centroid inequality for star bodies , Adv. in Appl. Math., 48 (2012), 432-445
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B. C. Zhu, N. Li, J. Z. Zhou, Isoperimetric inequalities for Lp-geominimal surface area, Glasgow Math. J., 53 (2011), 717-726
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B. C. Zhu, J. Z. Zhou, W. X. Xu , Lp mixed geominimal surface area, J. Math. Anal. Appl., 422 (2015), 1247-1263
]
Oscillation of strongly noncanonical equations
Oscillation of strongly noncanonical equations
en
en
New oscillation criteria for third order noncanonical differential equations of the form
\[
\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'+p(t)y(\tau(t))=0
\]
are established.
Our technique employs an equivalent canonical representation of the studied equation, which essentially simplifies the examination of noncanonical equations. The results obtained are supported by several illustrative examples.
1124
1128
Blanka
Baculikova
Department of Mathematics, Faculty of Electrical Engineering and Informatics
Technical University of Košice
Slovakia
blanka.baculikova@tuke.sk
Oscillation
third order differential equations
noncanonical operator
Article.2.pdf
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J. Džurina, Comparison theorems for nonlinear ODE’s, Math. Slovaca, 42 (1992), 299-315
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]
Numerical methods for solving initial value problems of some kinds of nonlinear impulsive fractional differential equations
Numerical methods for solving initial value problems of some kinds of nonlinear impulsive fractional differential equations
en
en
This article is concerned with the numerical solutions for initial value problems of nonlinear impulsive fractional differential equations which are actively studied recently. In this paper we construct numerical schemes for solving initial value problems of I-type impulsive fractional differential equation and II-type impulsive fractional differential equation and estimate their convergence and stability.
1129
1148
Yuanfeng
Jin
Department of Mathematics
Yanbian University
China
yfkim@ybu.edu.cn
Choehui
Chol
Department of Mathematics
Kim Il-sung University
DPRK
1214181195@qq.com
Paksun
Ae
Department of Mathematics
Kim Il-sung University
DPRK
1060208723@qq.com
Jongkum
Song
Department of Mathematics
Kim Il-sung University
DPRK
1179667503@qq.com
Gang
Lu
Department of Mathematics, School of Science
Shenyang University of Technology
China
lvgang1234@hanmail.net
Caputo fractional derivative
impulsive fractional differential equation
difference method
operational matrix method
decomposition method
Article.3.pdf
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M. Benchohra, D. Seba, Impulsive fractional differential equations in Banach spaces, Electron. J. Qual. Theory Differ. Equ., 2009 (2009), 1-14
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M. Feckan, Y. Zhou, J. R. Wang, On the concept and existence of solution for impulsive fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 3050-3060
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V. E. Tarasov, Fractional dynamics, Springer, (2010), -
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J. R. Wang, X. Z. Li, W. Wei, On the natural solution of an impulsive fractional differential equation of order q 2 (1, 2), Commun. Nonlinear Sci. Numer. Simul., 17 , 4384–4394. (2012)
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G. T. Wang , L. H. Zhang, G. X. Song, Systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions, Nonlinear Anal., 74 (2011), 974-982
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]
Existence and uniqueness of weak positive solution for essential singular elliptic problem involving the square root of the Laplacian
Existence and uniqueness of weak positive solution for essential singular elliptic problem involving the square root of the Laplacian
en
en
In this paper we consider the existence and uniqueness
of weak positive solution for nonlocal equations of the square root of the Laplacian with singular nonlinearity. The remarkable feature of this paper is the fact that the natural associated functional fails to be Frechet differentiable, critical point theory could not be applied to obtain the existence of weak positive solution. We first establish the priori estimate of weak solution of approximating problems. Then the weak positive solution is constructed by combining sub-and supersolutions method and truncate technology.
1149
1160
Xing
Wang
School of Science
Xi'an University of Technology
P. R. China
xj19856@sina.com
Li
Zhang
School of Science
Chang'an University
P. R. China
Fractional Laplacian
essential singular nonlinearity
nondifferentiable functional
a priori estimate
Article.4.pdf
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D. Applebaum, Lévy processes-from probability to finance and quantum groups, Notices Amer. Math. Soc., 51 (2004), 1336-1347
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B. Barrios, I. De Bonis, M. Medina, I. Peral, Semilinear problems for the fractional Laplacian with a singular nonlinearity, Open Math., 13 (2015), 390-407
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X. Cabré, J. G. Tan, Positive solutions for nonlinear problems involving the square root of the Laplacian, Adv. Math, 224 (2010), 2052-2093
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L. Caffarelli, L. Silvestre , An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32 (2007), 1245-1260
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Y. Q. Fang, Existence, Uniqueness of positive solution to a fractional Laplacians with singular nonlinearity, Analysis of PDEs, 2014 (2014), 1-11
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N. Hirano, C. Saccon, N. Shioji, Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities, Adv. Differential Equations, 9 (2004), 197-220
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G. Molica Bisci, V. D. Radulescu, R. Servadei , Variational methods for nonlocal fractional problems, Cambridge University Press, Cambridge (2016)
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]
Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions
Inclusion theorems associated with a certain new family of asymptotically and statistically equivalent functions
en
en
The aim of this paper is to introduce and investigate some new
definitions which are interrelated to the notions of asymptotically \(
I_\lambda\)-statistical equivalence of multiple \(L\) and strongly
\(I_\lambda\)-asymptotic equivalence of multiple \(L\).
Indeed, instead of sequences, the
authors make use of two nonnegative real-valued Lebesgue measurable
functions in the open interval \((1,\infty)\) and present a series of
inclusion theorems associated with these new definitions. Furthermore, in
connection with one of the main results which are proven in this paper, a
closely-related \(open\) \(problem\) is posed for the interested reader.
1161
1170
H. M.
Srivastava
University of Victoria
Department of Medical Research
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada \(\&\) Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China
China Medical University Hospital, China Medical University
Canada
Taiwan, Republic of China
harimsri@math.uvic.ca
Ekrem
Savaş
department of Mathematics
Istanbul Ticaret (Commerce) University
Turkey
ekremsavas@yahoo.com
Richard F.
Patterson
Department of Mathematics and Statistics
University of North Florida
U. S. A.
rpatters@unf.edu
Ideals and filters
\(\mathcal{I}\)-statistical convergence
\(I_{\lambda}\)-statistical convergence
\(\lambda\)-statistical convergence
de la Vallée Poussin method
Article.5.pdf
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[1]
M. Aldhaifallah, K. S. Nisar, H. M. Srivastava, M. Mursaleen, Statistical \(\Lambda\)-convergence in probabilistic normed spaces, J. Funct. Spaces, 2017 (2017), 1-7
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N. L. Braha, V. Loku, H. M. Srivastava, \(\Lambda^2\)-Weighted statistical convergence and Korovkin and Voronovskaya type theorems, Appl. Math. Comput., 266 (2015), 675-686
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H. Cakalli, A study on statistical convergence, Funct. Anal. Approx. Comput., 1 (2009), 19-24
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J. Connor, E. Savaş, Lacunary statistical and sliding window convergence for measurable functions, Acta Math. Hungar, 145 (2015), 416-432
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U. Kadak, On weighted statistical convergence based on (p, q)-integers and related approximation theorems for functions of two variables, J. Math. Anal. Appl., 443 (2016), 752-764
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M. Mursaleen, \(\lambda\)-Statistical convergence, Math. Slovaca, 50 (2000), 111-115
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M. Mursaleen, A. Alotaibi, On \(\jmath\)-convergence in random 2-normed spaces, Math. Slovaca, 61 (2011), 933-940
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M. Mursaleen, V. Karakaya, M. Ertürk, F. Gürsoy, Weighted statistical convergence and its application to Korovkin type approximation theorem, Appl. Math. Comput., 218 (2012), 9132-9137
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M. Mursaleen, H. M. Srivastava, S. K. Sharma, Generalized statistically convergent sequences of fuzzy numbers, J. Intelligent Fuzzy Systems, 30 (2016), 1511-1518
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F. Nuray, \(\lambda\)-Strongly summable and \(\lambda\)-statistically convergent functions, Iranian J. Sci. Tech. Trans. A Sci., 34 (2010), 335-339
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R. F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Math., 6 (2003), 149-153
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A. Sahiner, M. Gurdal, S. Saltan, H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11 (2007), 1477-1484
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E. Savaş, A-sequence spaces in 2-normed space defined by ideal convergence and an Orlicz function, Abstr. Appl. Anal., 2011 (2011), 1-9
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E. Savaş, Generalized summability methods of functions using ideals, Proceedings of the International Conference on Advancements in Mathematical Sciences (Antalya, Turkey), 2015 (2015), 1-5
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E. Savaş, On some new sequence spaces in 2-normed spaces using ideal convergence and an Orlicz function, J. Inequal. Appl., 2010 (2010), 1-8
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E. Savaş, On generalized statistical convergence in random 2-normed space, Iran. J. Sci. Technol. Trans. A Sci., 36 (2012), 417-423
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E. Savaş, On \(\jmath\)-asymptotically lacunary statistical equivalent sequences, Adv. Difference Equ., 2013 (2013), 1-7
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R. Savaş, M. Basarir, (\(\sigma,\lambda\))-Asymptotically statistical equivalent sequences, Filomat, 20 (2006), 35-42
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E. Savaş, H. Gumuş, A generalization on \(\jmath\)-asymptotically lacunary statistical equivalent sequences, J. Inequal. Appl., 2013 (2013), 1-9
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H. M. Srivastava, M. Et, Lacunary statistical convergence and strongly lacunary summable functions of order \(\alpha\), Filomat, 31 (2017), 1573-1582
]
A new muth generated family of distributions with applications
A new muth generated family of distributions with applications
en
en
A new family of distributions called the Muth family of distributions is introduced and studied. Five special submodels of the proposed family are discussed. Some mathematical properties of the Muth family are studied. Explicit expressions for the probability weighted, moments, mean deviation and order statistics are investigated. Maximum likelihood procedure is used to estimate the unknown parameters. One real data set is employed to show the usefulness of the new family.
1171
1184
Abdullah M.
Almarashi
Statistics Department, Faculty of Science
King AbdulAziz University
Kingdom of Saudi Arabia
aalmarashi@kau.edu.sa
M.
Elgarhy
Vice Presidency for Graduate Studies and Scientific Research
University of Jeddah
Kingdom of Saudi Arabia
m_elgarhy85@yahoo.com
Muth distribution
Weibull distribution
moments
order statistics
maximum likelihood estimation
Article.6.pdf
[
[1]
T. H. M. Abouelmagd, S. Al-mualim, M. Elgarhy, A. Z. Afify, M. Ahmad, Properties of the four-parameter Weibull distribution and its Applications, Pakistan J. Statist., 33 (2017), 449-466
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A variety of dynamic inequalities on time scales with retardation
A variety of dynamic inequalities on time scales with retardation
en
en
In this paper, we will prove some new nonlinear retarded dynamic inequalities of Gronwall-Bellman type on time scales. These inequalities are of new forms compared with the existing results so far in the literature, which can be used as effective tools in the study of certain nonlinear retarded dynamic equations. Some special cases of our results contain continuous Gronwall-type inequalities and their discrete analogues. We also indicate some application examples to illustrate our results at the end.
1185
1206
A. A.
El-Deeb
Department of Mathematics, Faculty of Science
Al-Azhar University
Egypt
ahmedeldeeb@azhar.edu.eg
Wing-Sum
Cheung
Department of Mathematics
The University of Hong Kong
wscheung@hku.hk
Gronwall's inequality
Young's inequality
time scales
Article.7.pdf
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]
On the new double integral transform for solving singular system of hyperbolic equations
On the new double integral transform for solving singular system of hyperbolic equations
en
en
In this manuscript, we will introduce a new double transform called double Elzaki transform (modification of Smudu transform), where we will study this transform and their theorems on convergence. Also, we will discuss the double new transform and it is convergent. After that, we study the combination of this double transforms and the new method in order to solve the singular system of hyperbolic equations of anomalies in through the examples in this paper. We found that this method is very effective in solving these equations compared to other methods as they need only one step to get the exact solution, while the other methods need more steps.
1207
1214
A. A.
Alderremy
Mathematics Department, Faculty of Science
King Kalied University
Saudi Arabia
aaldramy@kku.edu.sa
Tarig. M.
Elzaki
Mathematics Department, Faculty of Sciences and Arts-Alkamil
Mathematics Department, Faculty of Science
University of Jeddah
Sudan University of Sciences and Technology
Saudi Arabia
Sudan
tfarah@ uj.edu.sa;tarig.alzaki@gmail.com
Double new integral
transform
convergence
nonlinear singular system of hyperbolic equations
Article.8.pdf
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