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Zbl 1170.47049
Takahashi, Wataru; Zembayashi, Kei
Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 1, A, 45-57 (2009). ISSN 0362-546X

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 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47N10 Appl. of operator theory in optimization, math. programming, etc.
49J40 Variational methods including variational inequalities

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

Cited in: Zbl 1203.47066 Zbl 1180.90334

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