Abstract
AbstractWe consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property.2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25
Highlights
Introduction and Preliminaries LetE be a real Banach space, E* the dual space of E and C a nonempty closed convex subset of E
Let E be a real Banach space, E* the dual space of E and C a nonempty closed convex subset of E
We denote EP(f) the solution set of the equilibrium problem (1.1)
Summary
Introduction and Preliminaries LetE be a real Banach space, E* the dual space of E and C a nonempty closed convex subset of E. The mapping T is said to be closed if for any sequence {xn} ⊂ C such that lim n→∞ They proved that if C is nonempty bounded closed and convex every asymptotically nonexpansive self-mapping T on C has a fixed point in uniformly convex Banach spaces.
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