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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:

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
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References:

[5] doi:10.2307/2032162 · Zbl 0050.11603
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[24] doi:10.1016/0022-247X(83)90112-9 · Zbl 0519.49010
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