Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings

Abstract

We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-j-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25

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.…”

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

“…With the aid of generalization projections, we establish a strong theorem in a strictly convex and uniformly smooth Banach space. The results obtained in this paper mainly improve the corresponding results in [15], [16], [19], [20], [23], [30]. In order to prove our main results, we also need the following lemmas.…”

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

“…Since bifunction equilibrium problem covers variational inequality problems, zero point problems, and variational inclusion problems, it has been investigated by many authors via fixed point algorithms; see, for example, [5,6,8,9,10], [13]- [17], [24]- [28], [30] and the references therein.…”