Abstract
AbstractWe introduce a new iterative method for finding a common element of the set of solutions of a generalized equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space and then prove that the sequence converges strongly to a common element of the two sets. Using this result, we prove several new strong convergence theorems in fixed point problems, variational inequalities, and equilibrium problems.
Highlights
Throughout this paper, let R denote the set of all real numbers, let N denote the set of all positive integer numbers, let H be a real Hilbert space, and let C be a nonempty closed convex subset of H
We introduce a new iterative scheme for finding a common element of the set of solutions of a general equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings and obtain a strong convergence theorem
Using the main result in this paper, we prove several new strong convergence theorems for finding the elements of Fix S ∩EP, Fix S ∩EP Φ, Fix S ∩EP Φ, T, and Fix S ∩VI C, A, respectively, where S : C → C is a nonexpansive mapping
Summary
Throughout this paper, let R denote the set of all real numbers, let N denote the set of all positive integer numbers, let H be a real Hilbert space, and let C be a nonempty closed convex subset of H. We introduce a new iterative scheme for finding a common element of the set of solutions of a general equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings and obtain a strong convergence theorem.
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