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Zbl 1172.54028
Karpagam, S.; Agrawal, Sushama
Best proximity point theorems for $p$-cyclic Meir--Keeler contractions. (English)
[J] Fixed Point Theory Appl. 2009, Article ID 197308, 9 p. (2009). ISSN 1687-1812/e

In [J.~Math.\ Anal.\ Appl.\ 323, No.\,2, 1001--1006 (2006; Zbl 1105.54021)], {\it A.\,A.\thinspace Eldered} and {\it P.\,Veeramani} introduced cyclic contraction maps and gave sufficient conditions for the existence and convergence of a unique best proximity for such map on a uniformly convex space. Further, this result was extended by {\it C.\,Di~Bari, T.\,Suzuki} and {\it C.\,Vetro} [Nonlinear Anal., Theory Methods Appl.\ 69, No.\,11 (A), 3790--3794 (2008; Zbl 1169.54021)]. In this paper, the authors give sufficient conditions for the existence and convergence of the best proximity point for contraction maps of the Meir--Keeler type for $p\geq 2$ which is an extension of the results given in [Di Bari et al.,\ loc.\,cit.]
[Hemant Kumar Nashine (Raipur)]

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
41A65 Abstract approximation theory

Keywords: best proximity point; fixed points; $p$-cyclic map; $p$-cyclic Meir-Keeler contractions

Citations: Zbl 1105.54021; Zbl 1169.54021

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