Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces

Abstract

MSC: 47H05 47H09 47H10 47J25 65J15 Keywords: Strong convergence Equilibrium problem Quasi-φ-nonexpansive mapping Banach spaceThe purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of two quasi-φ-nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of Banach spaces. Our results improve and extend the corresponding results announced by many others.

Generalized mixed equilibrium and fixed point problems in a Banach space

“…Theorem 2.1 mainly improve the corresponding results in [14], [15], [17] and [18]. The framework of the space is weak which do not require the uniform convexness.…”

“…Recently, the above nonlinear problems have been extensively studied based on iterative techniques; see [3], [6]- [10], [14]- [17], [19], [22]- [26] and the references therein. In this paper, we study generalized mixed equilibrium problem (1.1) based on a monotone projection technique without any compactness assumption.…”

Strong convergence of hybrid algorithms for fixed point and bifunction equilibrium problems in reflexive Banach spaces

“…The class of asymptotically quasi-φ-nonexpansive mappings, which covers the class of quasi-φ-nonexpansive mappings [18], was considered in Qin, Cho and Kang [19] and Agarwal and Qin [17]; see also Zhou, Gao and Tan [31]. Remark 1.3.…”

Some results on asymptotically quasi-phi-nonexpansive mappings in the intermediate sense and Ky Fan inequalities

“…The class of quasi-φ-nonexpansive mappings [21] is a generalization of relatively nonexpansive mappings [6]. The class of quasi-φ-nonexpansive mappings do not require the strong restriction that the fixed point set equals the asymptotic fixed point set.…”