Abstract
In this article, we present a new iteration method for finding a common element of the set of fixed points of p strict pseudocontractions and the set of solutions of equilibrium problems for pseudomonotone bifunctions without Lipschitz-type continuous conditions. The iterative process is based on the extragradient method and Armijo-type linesearch techniques. We obtain weak convergence theorems for the sequences generated by this process in a real Hilbert space.AMS 2010 Mathematics Subject Classification: 65 K10; 65 K15; 90 C25; 90 C33.
Highlights
Let C be a nonempty closed convex subset of a real Hilbert space H and f be a bifunction from C × C to R
It is clear that every monotone bifunction f is pseudomonotone
We introduce a new iteration method for finding a common element of the set of common fixed points of p strict pseudocontractions and the set of solutions of equilibrium problems for pseudomonotone bifunctions
Summary
Let C be a nonempty closed convex subset of a real Hilbert space H and f be a bifunction from C × C to R. For finding a common element of the set of common fixed points of a strict pseudocontraction sequence {Si} and the set of solutions of Problem EP (f, C), Chen et al [9] proposed new iterative scheme in a real Hilbert space. ≥ 0, ∀y ∈ C, ||xn − v||}, they showed that under certain appropriate conditions imposed on {an} and {rn}, the sequences {xn}, {yn} and {zn} converge strongly to PrFix(S)∩Sol(f,C)(x0), where S is a mapping of There exist some another solution methods for finding a common element of the set of solutions of Problem EP(f, C) and ∩pi=1Fix(Si) (see [3,10,11,12,13,14,15,16,17,18,19]). We are in a position to describe the extragradient-Armijo algorithm for finding a common element of ∩pi=1 Fix (Si) ∩ Sol f , C
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