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Zbl 1187.47054
Takahashi, Wataru; Zembayashi, Kei
Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings. (English)
[J] Fixed Point Theory Appl. 2008, Article ID 528476, 11 p. (2008). ISSN 1687-1812/e

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 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H09 Mappings defined by "shrinking" properties
47N10 Appl. of operator theory in optimization, math. programming, etc.
65J15 Equations with nonlinear operators (numerical methods)

Keywords: strong convergence; equilibrium problem; relatively nonexpansive mapping; hybrid method

Cited in: Zbl 1205.47062 Zbl 1203.47066 Zbl 1187.47052 Zbl 1219.49010

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