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Strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces. (English) Zbl 1211.65063
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:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
47N10Applications of operator theory in optimization, convex analysis, programming, economics
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