Abstract
In this paper, the problem of approximating a common element in the common fixed point set of an infinite family of nonexpansive mappings, in the solution set of a variational inequality involving an inverse-strongly monotone mapping and in the solution set of an equilibrium problem is investigated based on a general iterative algorithm. Strong convergence of the iterative algorithm is obtained in the framework of Hilbert spaces. The results obtained in this paper improve the corresponding results announced by many authors.
Highlights
Introduction and preliminaries LetH be a real Hilbert space, whose inner product and norm are denoted by ·, · and · respectively
For solving the equilibrium problem ( . ), let us assume that F satisfies the following conditions: (A ) F(x, x) = for all x ∈ C; (A ) F is monotone, i.e., F(x, y) + F(y, x) ≤ for all x, y ∈ C; (A ) for each x, y, z ∈ C, lim sup F tz + ( – t)x, y ≤ F(x, y); t↓
In this paper, based on a general iterative algorithm, we study the problem of approximating a common element in the common fixed point set of an infinite family of nonexpansive mappings, in the solution set of a variational inequality involving an inversestrongly monotone mapping and in the solution set of an equilibrium problem
Summary
Introduction and preliminaries LetH be a real Hilbert space, whose inner product and norm are denoted by ·, · and · respectively.
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