Abstract
In this paper, a new iterative process by the hybrid projection method is constructed. Strong convergence of the iterative process to a common element of the set of common fixed points of a finite family of generalized nonexpansive multivalued mappings and the solution set of two equilibrium problems in a Hilbert space is proved. Our results extend some important recent results.
Highlights
Let C be a nonempty closed convex subset of a Hilbert space H
We denote by CB(C) and P(C) the collection of all nonempty closed bounded subsets and nonempty proximal bounded subsets of C, respectively
It is obvious that every nonexpansive multivalued mapping satisfies the condition (P)
Summary
Let C be a nonempty closed convex subset of a Hilbert space H. We modify this condition for multivalued mappings as follows (see [ ]): Definition . A multivalued mapping T : H → CB(H) is said to satisfy the condition (P) provided that It is obvious that every nonexpansive multivalued mapping satisfies the condition (P).
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