]>
2018
11
9
ISSN 2008-1898
97
Nonlocal initial and boundary value problems via fractional calculus with exponential singular kernel
Nonlocal initial and boundary value problems via fractional calculus with exponential singular kernel
en
en
In this paper, we investigate the existence and uniqueness of solutions for nonlocal initial and boundary value problems of exponential fractional differential equations, by applying standard fixed point theorems. Enlightening examples are also presented.
1015
1030
Sotiris K.
Ntouyas
Department of Mathematics
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
University of Ioannina
King Abdulaziz University
Greece
Saudi Arabia
sntouyas@uoi.gr
Jessada
Tariboon
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
Centre of Excellence in Mathematics
King Mongkut’s University of Technology North Bangkok
CHE
Thailand
Thailand
jessada.t@sci.kmutnb.ac.th
Chalong
Sawaddee
Department of Applied Mathematics and Statistics, Faculty of Sciences and Liberal Arts
Rajamangala University of Technology Isan
Thailand
chalong07@yahoo.com
Exponential fractional integral
exponential fractional derivative
nonlocal initial value problems
nonlocal boundary value problems
fixed point theorems
Article.1.pdf
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]
Convergence analysis of generalized viscosity implicit rules for a nonexpansive semigroup with gauge functions
Convergence analysis of generalized viscosity implicit rules for a nonexpansive semigroup with gauge functions
en
en
In this paper, we introduce an iterative algorithm for finding the set of common fixed points of nonexpansive semigroups by the generalized viscosity implicit rule in certain Banach spaces which has a uniformly Gateaux differentiable norm and admits the duality mapping \(j_\varphi\), where \(\varphi\) is a gauge function. We prove strong convergence theorems of proposed algorithm under appropriate conditions. As applications, we apply main result to solving the fixed point problems of countable family of nonexpansive mappings and the problems of zeros of accretive operators. Furthermore, we give some numerical examples for supporting our main results.
1031
1044
Pongsakorn
Sunthrayuth
Department of Mathematics and Computer Science, Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi (RMUTT)
Thailand
pongsakorn_su@rmutt.ac.th
Nuttapol
Pakkaranang
KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
King Mongkut’s University of Technology Thonburi (KMUTT)
Thailand
nuttapol.pak@mail.kmutt.ac.th
Poom
Kumam
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, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Facuty of Science
Department of Medical Research
King Mongkut’s University of Technology Thonburi (KMUTT)
King Mongkut’s University of Technology Thonburi (KMUTT)
China Medical University Hospital, China Medical University
Thailand
Thailand
Taiwan
poom.kum@kmutt.ac.th
Nonexpansive semigroup
Banach spaces
strong convergence
fixed point problem
iterative method
Article.2.pdf
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]
On the local convergence of Gargantini-Farmer-Loizou method for simultaneous approximation of multiple polynomial zeros
On the local convergence of Gargantini-Farmer-Loizou method for simultaneous approximation of multiple polynomial zeros
en
en
The paper deals with a well known iterative method for simultaneous computation of all zeros (of known multiplicities) of a polynomial
with coefficients in a valued field.
This method was independently introduced by Farmer and Loizou [M. R. Farmer, G. Loizou,
Math. Proc. Cambridge Philos. Soc., \({\bf 82}\) (1977), 427--437] and Gargantini [I. Gargantini,
SIAM J. Numer. Anal., \({\bf 15}\) (1978), 497--510].
If all zeros of the polynomial are simple, the method coincides with the famous Ehrlich's method [L. W. Ehrlich,
Commun. ACM, \({\bf 10}\) (1967), 107--108].
We provide two types of local convergence results for the Gargantini-Farmer-Loizou method.
The first main result improves the results of [N. V. Kyurkchiev, A. Andreev, V. Popov, Ann. Univ. Sofia Fac. Math. Mech., \({\bf 78}\) (1984), 178--185] and [A. I. Iliev, C. R. Acad. Bulg. Sci., \({\bf 49}\) (1996), 23--26] for this method.
Both main results of the paper generalize the results of Proinov [P. D. Proinov, Calcolo, \({\bf 53}\) (2016), 413--426] for Ehrlich's method.
The results in the present paper are obtained by applying a new approach for convergence analysis of Picard type iterative methods
in finite-dimensional vector spaces.
1045
1055
Petko D.
Proinov
Faculty of Mathematics and Informatics
University of Plovdiv Paisii Hilendarski
Bulgaria
proinov@uni-plovdiv.bg
Iterative methods
simultaneous methods
Ehrlich method
multiple polynomial zeros
Gargantini-Farmer-Loizou method
local convergence
error estimates
Article.3.pdf
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L. W. Ehrlich, A modified Newton method for polynomials, Commun. ACM, 10 (1967), 107-108
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A. J. Engler, A. Prestel, Valued Fields, Springer Monographs in Mathematics, Berlin (2005)
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M. S. Petković, B. Neta, L. D. Petković, J. Džunić, Multipoint methods for solving nonlinear equations, Elsevier/ Academic Press, Amsterdam (2013)
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P. D. Proinov, New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems, J. Complexity, 26 (2010), 3-42
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P. D. Proinov, General convergence theorems for iterative processes and applications to the Weierstrass root-finding method, J. Complexity, 33 (2016), 118-144
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P. D. Proinov, A general semilocal convergence theorem for simultaneous methods for polynomial zeros and its applications to Ehrlich’s and Dochev-Byrnev’s methods, Appl. Math. Comput., 284 (2016), 102-114
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P. D. Proinov, On the local convergence of Ehrlich method for numerical computation of polynomial zeros, Calcolo, 53 (2016), 413-426
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P. D. Proinov, Unified convergence analysis for Picard iteration in n-dimensional vector spaces, Calcolo, 2018 (2018), 1-21
##[21]
P. D. Proinov, S. I. Cholakov, Convergence of Chebyshev-like method for simultaneous approximation of multiple polynomial zeros, C. R. Acad. Bulg. Sci., 67 (2014), 907-918
##[22]
P. D. Proinov, M. T. Vasileva, On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously, J. Inequal. Appl., 2015 (2015), 1-25
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S. Tashev, N. Kyurkchiev, Certain modifications of Newton’s method for the approximate solution of algebraic equations, Serdica Bulg. Math. Publ., 9 (1983), 67-73
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P. Tilli, Convergence conditions of some methods for the simultaneous computation of polynomial zeros, Calcolo, 35 (1998), 3-15
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D. R. Wang, F. G. Zhao, Complexity analysis of a process for simultaneously obtaining all zeros of polynomials, Computing, 43 (1989), 187-197
]
Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications
Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications
en
en
In this paper, we introduce the concept of a cyclic \((\alpha,\beta)\)-admissible mapping type \(S\) and the notion of an \((\alpha,\beta)$-$(\psi,\varphi)\)-contraction type \(S\).
We also establish fixed point results for such contractions along with the cyclic \((\alpha,\beta)\)-admissibility type \(S\) in complete \(b\)-metric spaces
and provide some examples for supporting our result. Applying our new results, we obtain fixed point results for cyclic mappings and multidimensional fixed point results.
As application, the existence of a solution of the nonlinear integral equation is discussed.
1056
1069
Chirasak
Mongkolkeha
Department of Mathematics, Statistics and Computer Sciences, Faculty of Liberal Arts and Science
Kasetsart University, Kamphaeng-Saen Campus
Thailand
faascsm@ku.ac.th
Wutiphol
Sintunavarat
Department of Mathematics and Statistics, Faculty of Science and Technology
Thammasat University Rangsit Center
Thailand
wutiphol@mathstat.sci.tu.ac.th
\(\alpha\)-admissible mappings
cyclic \((\alpha,\beta)\)-admissible mappings
generalized weak contraction mappings
multidimensional fixed points
nonlinear integral equations
Article.4.pdf
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]
Relative strongly harmonic convex functions and their characterizations
Relative strongly harmonic convex functions and their characterizations
en
en
In this paper, we introduce a new class of harmonic convex functions
with respect to an arbitrary non-negative function, which is called
the strongly general harmonic convex function. We discuss some
characterizations of strongly general harmonic convex functions.
Relationship with other classes of convex functions are also
discussed. Some special cases are discussed as applications of the
main results. The ideas and techniques of this paper may be starting
point for further research.
1070
1076
Bandar
Bin-Mohsin
Department of Mathematics
King Saud University
Saudi Arabia
balmohsen@ksu.edu.sa
Muhammad
Aslam Noor
Department of Mathematics
Department of Mathematics
King Saud University
COMSATS Institute of Information Technology
Saudi Arabia
Pakistan
noormaslam@gmail.com
Khalida Inayat
Noor
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
khalidanoor@hotmail.com
Sabah
Iftikhar
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
sabah.iftikhar22@gmail.com
Harmonic convex function
strongly harmonic convex function
strongly general convex functions
Article.5.pdf
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M. A. Noor, K. I. Noor, Some Implicit Methods for Solving Harmonic Variational Inequalities, Inter. J. Anal. Appl., 12 (2016), 10-14
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M. A. Noor, K. I. Noor, S. Iftikhar, Hermite-Hadamard inequalities for strongly harmonic convex functions, J. Inequal. Spec. Funct., 7 (2016), 99-113
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M. A. Noor, K. I. Noor, S. Iftikhar, Inequalities via strongly p-harmonic log-convex functions, J. Nonl. Funct. Anal., 2017 (2017), 1-14
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M. A. Noor, K. I. Noor, S. Iftikhar, Integral inequalities for differentiable relative harmonic preinvex functions (survey), TWMS J. Pure Appl. Math., 7 (2016), 3-19
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M. A. Noor, K. I. Noor, S. Iftikhar, M. U. Awan, Strongly generalized harmonic convex functions and integral inequalities, J. Math. Anal., 7 (2016), 66-77
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On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations
On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations
en
en
In this paper, the application of adaptive generalized polynomial chaos (gPC) to quantify the uncertainty for non-linear random difference equations is analyzed. It is proved in detail that, under certain assumptions, the stochastic Galerkin projection technique converges algebraically in mean square to the solution process of the random recursive equation. The effect of the numerical errors on the convergence is also studied. A full numerical experiment illustrates our theoretical findings and gives useful insights to reduce the accumulation of numerical errors in practice.
1077
1084
J.
Calatayud
Instituto Universitario de Matemática Multidisciplinar
Universitat Politècnica de València
Spain
jucagre@alumni.uv.es
J.-C.
Cortés
Instituto Universitario de Matemática Multidisciplinar
Universitat Politècnica de València
Spain
jccortes@imm.upv.es
M.
Jornet
Instituto Universitario de Matemática Multidisciplinar
Universitat Politècnica de València
Spain
marjorsa@doctor.upv.es
Adaptive gPC
stochastic Galerkin projection technique
non-linear random difference equations
uncertainty quantification
numerical analysis
Article.6.pdf
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]
Strong and weak convergence of Mann iteration of monotone \(\alpha\)-nonexpansive mappings in uniformly convex Banach spaces
Strong and weak convergence of Mann iteration of monotone \(\alpha\)-nonexpansive mappings in uniformly convex Banach spaces
en
en
In this paper, the demiclosed principle of monotone \(\alpha\)-nonexpansive mapping is showed in a uniformly convex Banach space with the partial order ``\(\leq\)". With the help of such a demiclosed principle, the strong convergence of Mann iteration of monotone \(\alpha\)-nonexpansive mapping \(T\) are proved without some compact conditions such as semi-compactness of \(T\), and the weakly convergent conclusions of such an iteration are studied without the conditions such as Opial's condition. These convergent theorems are obtained under the iterative coefficient satisfying the condition, \[\sum\limits_{k=1}^{+\infty}\min\{\alpha_k,(1-\alpha_k)\}=+\infty,\]
which contains \(\alpha_k=\frac1{k+1}\) as a special case
1085
1095
Yuchun
Zheng
College of Statistics and Mathematics
School of Mathematics and Information Science
Yunnan University of Finance and Economics
Henan Normal University
P. R. China
P. R. China
zhengyuchun@htu.cn
Lin
Wang
College of Statistics and Mathematics
Yunnan University of Finance and Economics
P. R. China
WL64mail@aliyun.com
Ordered Banach space
fixed point
monotone \(\alpha\)-nonexpansive mapping
strong convergence
Article.7.pdf
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Coincidence for morphisms based on compactness principles
Coincidence for morphisms based on compactness principles
en
en
We present some general
coincidence results based on coincidence principles for compact
morphisms.
1096
1098
Donal
O'Regan
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
Ireland
donal.oregan@nuigalway.ie
Coincidence
noncompact morphisms
Article.8.pdf
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D. O’Regan, Coincidence theory for compact morphisms, Fixed Point Theory Appl., 2017 (2017), 1-8
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D. O’Regan, A note on coincidence theory for noncompact morphisms, Nonlinear Anal. Forum, (to appear.), -
]
A new generalization of Weibull-exponential distribution with application
A new generalization of Weibull-exponential distribution with application
en
en
In this article, we will introduce a new five-parameter continuous model, called the Kumaraswamy Weibull exponential distribution based on Kumaraswamy Weibull-G family [A. S. Hassan, M. Elgarhy, Adv. Appl. Stat., \({\bf 48}\) (2016), 205--239]. The new model contains some new distributions as well as some former distributions. Various mathematical properties of this distribution are studied. General explicit expressions for the quantile function, expansion of distribution and density functions, moments, generating function, incomplete moments, conditional moments, residual life function, reversed residual life function, mean deviation, inequality measures, Rényi and q-entropies, probability weighted moments, and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. The practical importance of the new distribution is demonstrated through real data sets where we compare it with several lifetime distributions.
1099
1112
Ramadan A.
ZeinEldin
Deanship of Scientific Research
Institute of Statistical Studies and Research
Deanship of Scientific Research
Cairo University
Kingdom of Saudi Arabia
Egypt
rzainaldeen@kau.edu.sa
M.
Elgarhy
Vice Presidency for Graduate Studies and Scientific Research
University of Jeddah
Kingdom of Saudi Arabia
m_elgarhy85@yahoo.com
Exponential distribution
Kumaraswamy Weibull-G family of distributions
moments
order statistics
maximum likelihood estimation
Article.9.pdf
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