Asymptotically Non-Expansive Actions of Topological Semigroups and Fixed Points

Holmes, R. D.; Lau, Anthony To-Ming

doi:10.1112/blms/3.3.343

Cited by 28 publications

(15 citation statements)

References 6 publications

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“…In the compact case, on the other hand, the requirement that S be commutative has been relaxed to the assumption that S be a left reversible semigroup. See Takahashi [17], Mitchell [16], Holmes and Lau [9,10]. Our approach to Theorem 1 is very different from that of these references (except [6]) in that we completely avoid the use of normal structure.…”

Section: Suppose C Has Both the Fixed Point Property And The Conditiomentioning

confidence: 94%

A common fixed point theorem for a commuting family of nonexpansive mappings

Bruck¹

1974

Pacific J. Math.

126

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It is shown that if a closed convex subset C of a Banach space has both the fixed point property and the conditional fixed point property for nonexpansive mappings and C is either weakly compact or bounded and separable, then any commuting family of nonexpansive self-mappings of C has a common fixed point. The set of common fixed points is a nonexpansive retract of C. Introduction* Let E be a real or complex Banach space and C a nonempty closed convex subset of E. Our purpose is to prove the following generalization of the DeMarr-Browder-Belluce-Kirk-Lim [8, 4, 1, 2, 15] fixed point theorem:

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Section: Suppose C Has Both the Fixed Point Property And The Conditiomentioning

confidence: 94%

A common fixed point theorem for a commuting family of nonexpansive mappings

Bruck¹

1974

Pacific J. Math.

126

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“…Lau has shown that this action is asymptotically non-expansive, but it is not non-expansive (g ruins everything!) [7]. For the sake of completeness we give the details of asymptotic non-expansivity and then we show that the action is not even semi-asymptotic non-expansive.…”

Section: Takahashi's Theorem For General Semi-topological Semigroupmentioning

confidence: 94%

“…DeMarr's theorem has been generalized in several directions by Belluce and Kirk [2,3], Takahashi [16], Mitchell [14], Lau and Holmes [7,8].…”

Section: Introductionmentioning

confidence: 99%

Semi-Asymptotic Non-Expansive Actions of Semi-Topological Semigroups

Amini¹,

Medghalchi²,

Naderi³

2016

Bulletin of the Korean Mathematical Society

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“…The author would like to express the most sincere thanks to the referees for their careful reading of the manuscript, important comments and the citation of Ref. [13]. The author is also very grateful to Professor Anthony Lau for giving valuable remarks and Refs.…”

Section: Acknowledgementsmentioning

confidence: 99%

Nonexpansive semigroups in CAT ( κ ) spaces

Huang

2014

Fixed Point Theory Appl

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The main purpose of this paper is to study Browder type convergence theorems for a nonexpansive semigroup with geometric approaches in a CAT(κ) space. Besides, we determine a necessary and sufficient condition for convergence of a Browder type iteration associated to a uniformly asymptotically regular nonexpansive semigroup on the unit sphere in an infinite-dimensional Hilbert space. MSC: 47H20; 47H10

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Asymptotically Non-Expansive Actions of Topological Semigroups and Fixed Points

Cited by 28 publications

References 6 publications

A common fixed point theorem for a commuting family of nonexpansive mappings

A common fixed point theorem for a commuting family of nonexpansive mappings

Semi-Asymptotic Non-Expansive Actions of Semi-Topological Semigroups

Nonexpansive semigroups in CAT ( κ ) spaces

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