Abstract
In this article, we introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed generalized quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of equilibrium problem in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.
Highlights
Introduction and preliminary LetE be a Banach space with the dual E*
The class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [4] in 1972. They proved that, if C is a nonempty bounded closed convex subset of a uniformly convex Banach space E, every asymptotically nonexpansive selfmapping T of C has a fixed point
In this article, inspired and motivated by the works mentioned above, we introduce an iterative process for finding a common element of the set of common fixed points of a finite family of closed generalized quasi-j-asymptotically nonexpansive mappings and the solution set of equilibrium problem in Banach spaces
Summary
Introduction and preliminary LetE be a Banach space with the dual E*. Let C be a nonempty closed convex subset of E and f :C × C ® R a bifunction, where R is the set of real numbers. Let C be a nonempty closed convex subset of a Banach space E and T : C ® C a mapping. They proved that, if C is a nonempty bounded closed convex subset of a uniformly convex Banach space E, every asymptotically nonexpansive selfmapping T of C has a fixed point.
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