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Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces. (English) Zbl 1170.47049
Summary: We introduce two iterative sequences 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 a Banach space. Then we study the strong and weak convergence of the sequences.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47N10Applications of operator theory in optimization, convex analysis, programming, economics
49J40Variational methods including variational inequalities
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References:
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