Abstract
AbstractThe purpose of this paper is to consider a shrinking projection method for finding the common element of the set of common fixed points for nonexpansive semigroups, the set of common fixed points for an infinite family of a "Equation missing"-strict pseudocontraction, the set of solutions of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion problem. Strong convergence of the sequences generated by the proposed iterative scheme is obtained. The results presented in this paper extend and improve some well-known results in the literature.
Highlights
Throughout this paper, we assume that H be a real Hilbert space with inner product ·, · and norm ·, and let C be a nonempty closed convex subset of H
In 2010, Katchang and Kumam 27 obtained a strong convergence theorem for finding a common element of the set of fixed points of a family of finitely nonexpansive mappings, the set of solutions of a mixed equilibrium problem and the set of solutions of a variational inclusion problem for an inverse-strongly monotone mapping
Kumam et al 28 proved a strongly convergence theorem of the iterative sequence generated by the shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of fixed points of a finite family of quasinonexpansive mappings, and the set of solutions of variational inclusion problems
Summary
Throughout this paper, we assume that H be a real Hilbert space with inner product ·, · and norm · , and let C be a nonempty closed convex subset of H. Takahashi 23 introduced the following iterative scheme for finding a common element of the set of solution of generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space.
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