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A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS WITH (A, $\eta$)-MONOTONE MAPPINGS IN HILBERT SPACES
Shang, Meijuan,Qin, Xiaolong The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we introduce a system of nonlinear variational inclusions involving (A, $\eta$)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, $\eta$)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.
Shang, Meijuan,Su, Yongfu The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.1
In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extend and improve the corresponding results announced by many others.
A system of nonlinear variational inclusions with (A, η)-monotone mappings in Hilbert spaces
Meijuan Shang,Xiaolong Qin 영남수학회 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we introduce a system of nonlinear variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.
Meijuan Shang,Yongfu Su 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extend and improve the corresponding results announced by many others. In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extend and improve the corresponding results announced by many others.
Xiaolong Qin,Yongfu Su,Meijuan Shang 대한수학회 2008 대한수학회지 Vol.45 No.1
In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others. In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.
Qin, Xiaolong,Su, Yongfu,Shang, Meijuan Korean Mathematical Society 2008 대한수학회지 Vol.45 No.1
In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.
Strong Convergence Theorems for Asymptotically Nonexpansive Mappings by Hybrid Methods
Qin, Xiaolong,Su, Yongfu,Shang, Meijuan Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.1
In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.