Weak convergence theorems for a countable family of Lipschitzian mappings

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:230

Article

Nilsrakoo, Weerayuth¹  Saejung, Satit² 

[1] Ubon Rajathanee Univ, Dept Math Stat & Comp, Ubon Ratchathani 34190, Thailand

[2] Khon Kaen Univ, Dept Math, Khon Kaen 40002, Thailand

关键词: Weak convergence theorem;    Lipschitzian mapping;    Equilibrium problem;    Variational inequality problem;   

DOI  :  10.1016/j.cam.2008.12.013

来源: Elsevier

【 摘 要 】

This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We also establish weak convergence theorems for finding a common element of the set of fixed points, the set of solutions of an equilibrium problem, and the set of solutions of a variational inequality. With an appropriate setting, we obtain and improve the corresponding results recently proved by Moudafi [A. Moudafi, Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9(2008)37-43], Tada-Takahashi [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J. Optim. Theory Appl. 133 (2007) 359-370], and Plubtieng-Kumam [S. Plubtieng and P. Kumam, Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings. J. Comput. Appl. Math. (2008) doi:10.1016/j.cam.2008.05.045]. Some of our results are established with weaker assumptions. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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