Abstract
In this paper, we propose and analyze an explicit type algorithm for finding a common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two countable families of total quasi-φ-asymptotically nonexpansive mappings in a Banach space E. As an application of our result, we suggest a framework for finding a common solution of a finite family of generalized equilibrium problems and common zeros of two finite families of maximal monotone operators on E. MSC:47H05, 47H10, 47H15, 47J25, 49M05.
Highlights
Introduction and preliminaries LetE be a real Banach space with the norm · and E∗ be its dual
We denote by F(T) = {x ∈ C : x = Tx} the set of fixed points of T
Inspired and motivated by the work of Takahashi and Zembayashi [ ], Chang et al [ ] and Zuo et al [ ], we aim to introduce and analyze a general algorithm based on the shrinking projection method for finding a common element of the set of common solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two countable families of total quasi-φasymptotically nonexpansive mappings
Summary
Muhammad Aqeel Ahmad Khan1*, Hafiz Fukhar-ud-din[1,2] and Abdul Rahim Khan[2] Dedicated to Professor Wataru Takahashi on the occasion of his 70th birthday
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