Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces. (English) Zbl 1170.47049

Takahashi, Wataru; Zembayashi, Kei

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 1, 45-57 (2009).

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

Keywords:

Banach space; equilibrium problem; relatively nonexpansive mapping; strong convergence; weak convergence; resolvent

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