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Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings
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作者 Pham Ngoc Anh Tran Dinh Quoc Dang Xuan Son 《Applied Mathematics》 2012年第10期1357-1367,共11页
This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combi... This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions. 展开更多
关键词 EQUILIBRIUM Problems Fixed Point Pseudo-Monotone Lipschitz-Type CONTINUITY Extragradient Method STRICT pseudo-contraction mapping
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A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM 被引量:5
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作者 刘敏 张石生 《Acta Mathematica Scientia》 SCIE CSCD 2012年第2期499-519,共21页
In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseu... In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12]. 展开更多
关键词 k-strict pseudo-contractive mappings generalized equilibrium problem vis-cosity approximation method variational inclusion problem multi-valuedmaximal monotone mappings s-inverse-strongly monotone mapping
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APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES 被引量:2
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作者 Yekini SHEHU 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期409-423,共15页
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed poin... Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results. 展开更多
关键词 pseudo-contractive mappings reflexive Banach spaces uniformly Gateaux differentiable norm variational inequality
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SOME CONVERGENCE PROBLEM OF ITERATIVE SEQUENCESFOR ACCRETIVE AND PSEUDO-CONTRACTIVETYPE MAPPING IN BANACH SPACES
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作者 ZHANG Shi-sheng(张石生) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第4期394-408,共15页
Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, ... Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results. 展开更多
关键词 accretive mapping pseudo-contractive mapping hemi-accretive mapping hemi-pseudo-contractive mapping Ishikawa iterative sequence Mann iterative sequence steepest descent sequence
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CQ Method for Strictly Pseudo-Contractive Mapping
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作者 黄家琳 陈世群 《Journal of Southwest Jiaotong University(English Edition)》 2009年第4期355-358,共4页
This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-con... This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈ [0,1). 展开更多
关键词 k-Strictly pseudo-contractive mapping CQ method Metric projection ]
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NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY L-LIPSCHITZIAN MAPPINGS 被引量:5
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作者 谷峰 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期2058-2066,共9页
The purpose of this paper is to study necessary and su?cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Bana... The purpose of this paper is to study necessary and su?cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7]. 展开更多
关键词 asymptotically pseudo-contractive mapping uniformly L-Lipschitzian map- ping parallel iterative algorithm
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Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第2期145-152,共8页
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper e... The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people. 展开更多
关键词 Lipschitzian pseudo-contraction semi-group demi-closed principle common fixed point Opial condition strongly pseudo-contraction mapping implicit iteration process
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ON THE EXISTENCE OF SOLUTIONS FOR EQUATIONS WITH ACCRETIVE MAPPINGS IN PROBABILISTIC NORMED SPACES
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作者 张石生 陈玉清 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第9期821-828,共8页
The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN... The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN space and some existence theorems are shown. 展开更多
关键词 Accretive mapping probabilistic normed space pseudo-contractive mapping
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ITERATIVE PROCESS FOR CERTAIN NONLINEAR MAPPINGS WITH LIPSCHITZ CONDITION
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作者 GU Feng(谷峰) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第12期1458-1467,共10页
Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive m... Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive mappings are discussed. The main results of this paper improve and extend the corresponding results obtained by Chang, Chidume, Deng, Ding, Tan-Xu and Osilike. 展开更多
关键词 phi-strongly accretive operator phi-strongly pseudo-contractive mapping Ishikawa iterative sequence Mann iterative sequence
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A Modified Averaging Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of k-Strictly Asymptotically Pseudocontractive Mappings
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作者 Donatus Igbokwe Oku Ini 《Advances in Pure Mathematics》 2011年第4期204-209,共6页
The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-stric... The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process. 展开更多
关键词 IMPLICIT ITERATION Process k-Strictly ASYMPTOTICALLY pseudo-contractive maps Fixed POINTS
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Three-step Iterations with Errors for Nonlinear Strongly Accretive Operator Equations 被引量:2
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作者 Ke Su 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2005年第4期565-570,共6页
In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper imp... In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper improve and extend current results in the more general setting. 展开更多
关键词 Three-step iteration process with errors strongly accretive mapping strongly pseudo-contractive mapping uniformly smooth Banach space
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