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Common best proximity pairs in strictly convex Banach spaces

  • Moosa Gabeleh EMAIL logo
Published/Copyright: May 20, 2016
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Abstract

A mapping T:ABAB such that T(A)A and T(B)B is called a noncyclic mapping, where A and B are two nonempty subsets of a Banach space X. A best proximity pair (p,q)A×B for such a mapping T is a point such that p=Tp,q=Tq and p-q=dist(A,B). In the current paper, we establish some existence results of best proximity pairs in strictly convex Banach spaces. The presented theorems improve and extend some recent results in the literature. We also obtain a generalized version of Markov–Kakutani’s theorem for best proximity pairs in a strictly convex Banach space setting.

MSC 2010: 47H10; 47H09; 46B20

Funding statement: The author was partially supported by a grant from IPM (No. 94470047).

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Received: 2014-8-1
Revised: 2014-11-28
Accepted: 2015-1-12
Published Online: 2016-5-20
Published in Print: 2017-9-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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