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Fixed Point Theorems for Lipspchitzian Semigroups

Published online by Cambridge University Press:  20 November 2018

Hajime ishihara
Hajime ishihara*
Affiliation:
Department of Information Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan
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Abstract

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Let U be a nonempty subset of a Banach space, S a left reversible semitopological semigroup, a continuous representation of S as lipschitzian mappings on U into itself, that is for each s ∊ S, there exists ks > 0 such that for x, y ∊ U. We first show that if there exists a closed subset C of U such that then S with lim sups has a common fixed point in a Hilbert space. Next, we prove that the theorem is valid in a Banach space E if lim sups

Keywords

47H1054H25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 90 - 97
Copyright
Copyright © Canadian Mathematical Society 1989

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