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A modified projection method for a common solution of a system of variational inequalities, a split equilibrium problem and a hierarchical fixed-point problem

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fixed point THEORY AND APPLICATIONS 2014年第1期2014卷 1-25页

作者： Bnouhachem, Abdellah Nanjing Univ Sch Management Sci & Engn Nanjing 210093 Jiangsu Peoples R China Ibn Zohr Univ ENSA Agadir Morocco

In this paper, we suggest and analyze a modified projection method for finding a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem in the setting of real Hilbert spaces. We prove the strong convergence of the sequence generated by the proposed method to a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem. Several special cases are also discussed. The results presented in this paper extend and improve some well-known results in the literature.

关键词： system of variational inequalities equilibrium problem hierarchical fixed-point problem fixed-point problem projection method

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On solving the minimization problem and the fixed-point problem for nonexpansive mappings in CAT(0) spaces

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OPTIMIZATION METHODS & SOFTWARE 2017年第1期32卷 182-192页

作者： Suparatulatorn, Raweerote Cholamjiak, Prasit Suantai, Suthep Univ Phayao Sch Sci Phayao 56000 Thailand Chiang Mai Univ Fac Sci Dept Math Chiang Mai 50200 Thailand

We propose a new modified proximal point algorithm combined with Halpern's iteration process for nonexpansive mappings in the framework of CAT(0) spaces. We establish a strong convergence theorem under some mild c... 详细信息

关键词： convex minimization problem fixed-point problem CAT(0) space proximal point algorithm nonexpansive mapping

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The subgradient extragradient method for approximation of fixed-point problem and modification of equilibrium problem

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OPTIMIZATION 2023年第2期72卷 383-410页

作者： Saechou, Kanyanee Kangtunyakarn, Atid King Mongkuts Inst Technol Ladkrabang Fac Sci Dept Math Bangkok Thailand

In this paper, we consider the modification of equilibrium problem (MEP) and new subgradient extragradient algorithm by using the concept of the set of solutions of the modified variational inequality problem introduced by [Kangtunyakarn A. A new iterative scheme for fixed-point problems of infinite family of kappa(i) pseudo contractive mappings, equilibrium problem, variational inequality problems. J Optim Theory Appl. 2013;56:1543-1562.]. Then, we establish and prove weak and strong convergence theorem of the new subgradient extragradient algorithm for finding a common element of the set of solutions of the MEP and two sets of the variational inequality problems under some suitable conditions on alpha(n) and beta(n) with alpha(n) + beta(n) <= 1. Moreover, we apply our main theorem to prove weak and strong convergence theorems to solve the generalized equilibrium problem, the system of equilibrium problem, the variational inequality problem and the general system of variational inequality problems. Finally, we give two numerical examples to support our main result.

关键词： Equilibrium problem subgradient extragradient algorithm variational inequality problem fixed-point problem

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An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping

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OPTIMIZATION LETTERS 2014年第3期8卷 1113-1124页

作者： Kazmi, K. R. Rizvi, S. H. Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

In this paper, we introduce and study an iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping which is the unique solution of the variational inequality problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

关键词： Split variational inclusion problem Nonexpansive mapping fixed-point problem Averaged mapping Iterative method

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A hybrid extragradient method for approximating the common solutions of a variational inequality, a system of variational inequalities, a mixed equilibrium problem and a fixed point problem

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APPLIED MATHEMATICS AND COMPUTATION 2012年第9期218卷 5439-5452页

作者： Kazmi, K. R. Rizvi, S. H. Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

In this paper, we give a hybrid extragradient iterative method for finding the approximate element of the common set of solutions of a generalized equilibrium problem, a system of variational inequality problems, a variational inequality problem and a fixed point problem for a strictly pseudocontractive mapping in a real Hilbert space. Further we establish a strong convergence theorem based on this method. The results presented in this paper improves and generalizes the results given in Yao et al. [36] and Ceng et al. [7], and some known corresponding results in the literature. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Mixed equilibrium problem Variational inequality problem System of variational inequality problems Strictly pseudocontractive mappings fixed-point problem

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Implicit iterative method for approximating a common solution of split equilibrium problem and fixed point problem for a nonexpansive semigroup

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Arab Journal of Mathematical Sciences 2014年第1期20卷 57-75页

作者： Kazmi, K.R. Rizvi, S.H. Department of Mathematics Aligarh Muslim University Aligarh 202002 India

In this paper, we introduce and study an implicit iterative method to approximate a common solution of split equilibrium problem and fixed point problem for a nonexpansive semigroup in real Hilbert spaces. Further, we prove that the nets generated by the implicit iterative method converge strongly to the common solution of split equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. Furthermore, we justify our main result through a numerical example. The results presented in this paper extend and generalize the corresponding results given by Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, fixed point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces, Math. Comput. Model. 48 (2008) 279–286] and Cianciaruso et al. [F. Cianciaruso, G. Marino, L. Muglia, Iterative methods for equilibrium and fixed point problems for nonexpansive semigroups in Hilbert space, J. Optim. Theory Appl. 146 (2010) 491–509]. © 2013

关键词： Averaged mapping fixed-point problem Implicit iterative method Nonexpansive semigroup Primary 65K15 Secondary 47J25 65J15 90C33 Split equilibrium problem

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Iterative approximation of a common solution of split equilibrium, split variational inequality, and fixed point problem for a nonexpansive semigroup

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2022年第8期45卷 4343-4364页

作者： Rizvi, Shuja H. Sikander, Fahad Saudi Elect Univ Coll Sci & Theoret Studies Riyadh 11673 Saudi Arabia

The purpose of this work is to investigate an iterative method to find a common solution of a split equilibrium problem, split variational inequality problem involving inverse strongly monotone mappings, and fixed point problem for a nonexpansive semigroup in the framework of real Hilbert spaces. Under some mild conditions, strong convergence theorem is obtained. Further, some special cases of main result are also included. Furthermore, we provide some numerical experiments to justify our main result. The results presented in this work may be treated as an improvement, extension, and refinement of some corresponding ones in the literature.

关键词： fixed-point problem nonexpansive semigroup split equilibrium problem split variational inequality problem

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Iterative approximation of a common solution of a split equilibrium problem, a variational inequality problem and a fixed point problem

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Journal of the Egyptian Mathematical Society 2013年第1期21卷 44-51页

作者： K.R. Kazmi S.H. Rizvi Department of Mathematics Aligarh Muslim University Aligarh 202 002 India

In this paper, we introduce an iterative method to approximate a common solution of a split equilibrium problem, a variational inequality problem and a fixed point problem for a nonexpansive mapping in real Hilbert spaces. We prove that the sequences generated by the iterative scheme converge strongly to a common solution of the split equilibrium problem, the variational inequality problem and the fixed point problem for a nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area.

关键词： 49J30 47H10 47H17 90C99 Split equilibrium problem Variational inequality problem fixed-point problem Nonexpansive mapping Inverse-strongly monotone mapping

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A viscosity Cesàro mean approximation method for split generalized vector equilibrium problem and fixed point problem

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Journal of the Egyptian Mathematical Society 2015年第2期23卷 362-370页

作者： K.R. Kazmi S.H. Rizvi Mohd. Farid Department of Mathematics Aligarh Muslim University Aligarh 202002 India

In this paper, we introduce and study an explicit iterative method to approximate a common solution of split generalized vector equilibrium problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces using the viscosity Cesàro mean approximation. We prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Further we give a numerical example to justify our main result. The results presented in this paper generalize, improve and unify the previously known results in this area.

关键词： 49J30 47H10 47H17 90C99 Split generalized vector equilibrium problem fixed-point problem Nonexpansive mapping Viscosity cesàro mean approximation method

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fixed-point technique for implicit complementarity problem in Hilbert lattice

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1997年第1期93卷 67-72页

作者： Ahmad, K Kazmi, KR Rehman, N Department of Mathematics Faculty of Natural Sciences Jamia Millia Islamia New Delhi India

In this paper, we consider and study the implicit complementarity problem in the setting of a Hilbert lattice. It has been shown that this problem can be formulated as a fixed-point problem by using a suitable change of variables. Moreover, this formulation allows us to prove the existence and uniqueness of solutions of the implicit complementarity problem.

关键词： implicit complementarity problem change of variables fixed-point problem phi-Lipschitz continuous mapping psi-strongly monotone mapping

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