Abstract
We give a sufficient and necessary condition concerning a Browder's convergence type theorem for uniformly asymptotically regular one-parameter nonexpansive semigroups in Hilbert spaces.
Highlights
Let C be a closed convex subset of a Hilbert space E
We denote by F T the set of fixed points of T
See 1, proved that F T is nonempty provided that C is, in addition, bounded
Summary
Let C be a closed convex subset of a Hilbert space E. We denote by F T the set of fixed points of T. See 1 , proved that F T is nonempty provided that C is, in addition, bounded. Kirk in a very celebrated paper, see 2 , extended this result to the setting of reflexive Banach spaces with normal structure. Browder 3 initiated the investigation of an implicit method for approximating fixed points of nonexpansive self-mappings defined on a Hilbert space. Browder proved that limt → 0zt P u, where P u is the element of F T nearest to u. Extensions to the framework of Banach spaces of Browder’s convergence results have been done by many authors, including Reich 4 , Takahashi and Ueda 5 , and O’Hara et al 6
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