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:
47J25 | Iterative procedures involving nonlinear operators |
47H10 | Fixed-point theorems |
47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
47N10 | Applications of operator theory in optimization, convex analysis, mathematical programming, economics |
65J15 | Numerical solutions to equations with nonlinear operators |
References:
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