Abstract
We propose new iterative schemes for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solutions of the variational inequality problem for relaxed cocoercive and Lipschitz continuous, the set of solutions of system of variational inclusions problem, and the set of solutions of equilibrium problems in a real Hilbert space by using the viscosity approximation method. We prove strong convergence theorem under some parameters. The results in this paper unify and generalize some well‐known results in the literature.
Highlights
Let C be a nonempty closed convex subset of a real Hilbert space H
We propose new iterative schemes for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solutions of the variational inequality problem for relaxed cocoercive and Lipschitz continuous, the set of solutions of system of variational inclusions problem, and the set of solutions of equilibrium problems in a real Hilbert space by using the viscosity approximation method
In this paper, motivated and inspired by the above facts, we introduce a new iterative scheme for finding a common element of the set of solutions of the variational inequalities for μ-Lipschitz continuous and relaxed φ, ω -cocoercive mapping, the set of solutions to the variational inclusion for family of α-inverse strongly monotone mappings, the set of fixed points of a countable family of nonexpansive mappings, and the set of solutions of an equilibrium problem in a real Hilbert space by using the viscosity approximation method
Summary
Let C be a nonempty closed convex subset of a real Hilbert space H. In this paper, motivated and inspired by the above facts, we introduce a new iterative scheme for finding a common element of the set of solutions of the variational inequalities for μ-Lipschitz continuous and relaxed φ, ω -cocoercive mapping, the set of solutions to the variational inclusion for family of α-inverse strongly monotone mappings, the set of fixed points of a countable family of nonexpansive mappings, and the set of solutions of an equilibrium problem in a real Hilbert space by using the viscosity approximation method. Strong convergence results are derived under suitable conditions in a real Hilbert space
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