Semigroup of nonexpansive mappings on a Hilbert space
type: Item
instance of: scholarly article
title: Semigroup of nonexpansive mappings on a Hilbert space
zbMATH Open document ID: 0656.47049
DOI: 10.1016/0022-247X(85)90066-6
author: A. T.-M. Lau
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: A result of Opial states the following: ``Let X be a uniformly convex Banach space with a weakly continuous duality mapping and let C be a closed convex subset of X. If T:C\(\to C\) is a nonexpansive mapping having at least one fixed point and if \(\lim_{n\to \infty}\| T^ nx- T^{n-1}x\| =0\), then \(T^ ny\) converges weakly to a fixed point of T.'' The present author generalizes this result to right (or left) reversible semitopological semigroups of nonexpansive mappings. Other existence theorems on common fixed points are proved under certain assumptions of existence of an invariant mean and relative compactness or boundedness on the orbits.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 4071745
zbMATH Keywords: uniformly convex Banach space with a weakly continuous duality mapping
zbMATH Keywords: closed convex subset
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: reversible semitopological semigroups of nonexpansive mappings
zbMATH Keywords: existence theorems on common fixed points
MaRDI profile type: Publication
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full work available at URL: 0022-247x(85)90066-6
OpenAlex ID: W2069959706
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description: scientific article; zbMATH DE number 4071745