A new iterative method for equilibrium problems and fixed point problems of infinitely nonexpansive mappings and monotone mappings☆
Section snippets
Introduction and preliminaries
Let H be a real Hilbert space with inner product and norm . Let C be a nonempty closed convex subset of H and be a bifunction of into R, where R is the set of real numbers. The equilibrium problem for is to find such thatfor all . The set of solutions of (1.1) is denoted by . Given a mapping , let for all . Then if and only if for all , i.e., z is a solution of the variational inequality.
It is well
Main results
Theorem 2.1 Let C be a closed convex subset of a real Hilbert space H. Let F be a bifunction from satisfying (A1)–(A4), A be an -inverse-strongly monotone mapping of C into H and be a sequence of nonexpansive self-mappings on C such that . Suppose , are sequences in , is a sequence in such that for some with and is a real sequence. Suppose the following conditions are satisfied: ,
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This research is supported by Tianjin Natural Science Foundation in China Grant (06YFJMJC12500) and supported by the science research foundation program in Civil Aviation University of China (04-CAUC-15 S) as well.