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May 2018 Lim’s center and fixed-point theorems for isometry mappings
S. Rajesh, P. Veeramani
Ann. Funct. Anal. 9(2): 190-201 (May 2018). DOI: 10.1215/20088752-2017-0046

Abstract

In this article, we prove that if K is a nonempty weakly compact convex set in a Banach space such that K has the hereditary fixed-point property (FPP) and F is a commuting family of isometry mappings on K, then there exists a point in C(K) which is fixed by every member in F whenever C(K) is a compact set. Also, we give an example to show that C(K), the Chebyshev center of K, need not be invariant under isometry maps. This example answers the question as to whether the Chebyshev center is invariant under isometry maps. Furthermore, we give a simple example to illustrate that Lim’s center, as introduced by Lim, is different from the Chebyshev center.

Citation

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S. Rajesh. P. Veeramani. "Lim’s center and fixed-point theorems for isometry mappings." Ann. Funct. Anal. 9 (2) 190 - 201, May 2018. https://doi.org/10.1215/20088752-2017-0046

Information

Received: 25 December 2016; Accepted: 17 April 2017; Published: May 2018
First available in Project Euclid: 13 October 2017

zbMATH: 06873696
MathSciNet: MR3795084
Digital Object Identifier: 10.1215/20088752-2017-0046

Subjects:
Primary: 47H09 , 47H10

Keywords: asymptotic center , center of a convex set , Chebyshev center , isometry mappings

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 2 • May 2018
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