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Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings. (English) Zbl 1187.47054
Summary: We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution of an equilibrium problem and a fixed point of a relatively nonexpansive mapping in a Banach space.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
47N10Applications of operator theory in optimization, convex analysis, programming, economics
65J15Equations with nonlinear operators (numerical methods)
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