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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:
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
49J40 Variational inequalities
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