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Best proximity point theorems for $p$-cyclic Meir–Keeler contractions. (English) Zbl 1172.54028

In [J. Math. Anal. Appl. 323, No. 2, 1001–1006 (2006; Zbl 1105.54021)], A. A. Eldered and 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 C. Di Bari, T. Suzuki and 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 $p\ge 2$ which is an extension of the results given in [Di Bari et al., loc. cit.]

MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 41A65 Abstract approximation theory
References:
 [1] [2] [3] [4] [5] [6] [7] [8]