Best proximity points theorems for generalized mizoguchi-takahashi's contraction pairst
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Publication Details
Author list: Sintunavarat W., Kumam P.
Publisher: Yokohama Oublishers
Publication year: 2016
Journal: Journal of Nonlinear and Convex Analysis (1345-4773)
Volume number: 17
Issue number: 7
Start page: 1345
End page: 1361
Number of pages: 17
ISSN: 1345-4773
Languages: English-Great Britain (EN-GB)
Abstract
In this paper, we introduce the concept of a generalized Mizoguchi-Takahashi's contraction pairs for non-self mappings. We also study a best proximity point result for such type contraction pair in metric spaces and use this result to investigate the existence of best proximity point theorems in uniformly convex Banach spaces. We state some illustrative examples to support the generality of main result. Our results improve and extend a host of previously well-known results such as Nadler's fixed point theorem, Mizoguchi and Takahashi's fixed point theorem. ฉ 2016.
Keywords
Best proximity points, MT-function (or R-function), Multi-valued contraction
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