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Zbl 1211.65063
Zhang, Congjun; Li, Jinlu; Liu, Baoqing
Strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces. (English)
[J] Comput. Math. Appl. 61, No. 2, 262-276 (2011). ISSN 0898-1221

Summary: The purpose of the paper is to introduce modified Halpern and Ishikawa iteration for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in Banach spaces. We also consider two strong convergence theorems for relatively nonexpansive mappings with some proper restriction.

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)
47N10 Appl. of operator theory in optimization, math. programming, etc.

Keywords: equilibrium problem; relatively nonexpansive mapping; convergence theorem

Cited in: Zbl 1236.47074

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