Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems
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Author list: Kumam P., Aydi H., Karapinar E., Sintunavarat W.
Publisher: SpringerOpen
Publication year: 2013
Journal: Fixed Point Theory and Applications (1687-1820)
Volume number: 2013
ISSN: 1687-1820
eISSN: 1687-1812
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we introduce a multi-valued cyclic generalized contraction by extending the Mizoguchi and Takahashi's contraction for non-self mappings. We also establish a best proximity point for such type contraction mappings in the context of metric spaces. Later, we characterize this result to investigate the existence of best proximity point theorems in uniformly convex Banach spaces. We state some illustrative examples to support our main theorems. Our results extend, improve and enrich some celebrated results in the literature, such as Nadler's fixed point theorem, Mizoguchi and Takahashi's fixed point theorem. ฉ2013 Kumam et al.; licensee Springer.
Keywords
Best proximity points, Cyclic contraction, MT-function (or R-function), Multi-valued contraction
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