Some Results for Split Equality Equilibrium Problems in Banach Spaces

Abstract

In this paper, a new algorithm for finding a common element of a split equality fixed point problem for nonexpansive mappings and split equality equilibrium problem in three Banach spaces is introduced. Also, some strong and weak convergence theorems for the proposed algorithm are proved. Finally, the main results obtained in this paper are applied to solve the split equality convex minimization problem.

On split equality generalized equilibrium problems and fixed point problems of Bregman relatively nonexpansive semigroups

“…Finally, we present some numerical experiments to illustrate the applicability of our proposed method. The result obtained in this article generalizes the results of [22], [23], [24], and other related results in the literature.…”

“…If C := Fix(S) and Q := Fix(T ) in (1.6), where S : H 1 → H 1 and T : H 2 → H 2 are two nonlinear mappings, then the SEP becomes the Split Equality Fixed Point Problem (SEFPP). Following the idea of SFP (1.6), Ma et al [22] introduced the Split Equality Equilibrium Problem (SEEP) in Banach spaces. Let E 1 , E 2 , and E 3 be three Banach spaces, and let C and Q be nonempty, closed, and convex subsets of E 1 and E 2 , respectively.…”

“…We denote by SEEP(F, G), the set of solutions of SEEP (1.7). Furthermore, Ma et al [22] proved the following weak and strong convergence theorem for finding a common element in the set of solutions of the SEFPP with nonexpansive mappings and the set of solutions of the SEEP in three Banach spaces as follows.…”

An iterative scheme for split equality equilibrium problems and split equality hierarchical fixed point problem

“…As particular cases, SEP includes the split variational inequalities [7] and split feasibility problem [6], which have a wide range of applications; see [4,5,7,10,11,21,31,32]. SEEP (1.1)-(1.2) has been studied by many authors; see, for instance, Ma et al [23,24] and Ali et al [2] for monotone bifunctions g 1 , g 2 . It is interesting to study SEEP (1.1)-(1.2) when both bifunctions g 1 , g 2 are pseudomonotone.…”

A different approach to approximating solutions of monotone Yoshida variational inclusion problem in a Banach space

“…al. [25], Ogbuisi and Mewomo [24], we introduce an Halphern-type iterative method for approximating the solution of MYVIP (17) in the framework of p-uniformly convex and uniformly smooth Banach space. We prove a strong convergence theorem of the aforementioned problem.…”