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Displaying similar documents to “Results on the existence and convergence of best proximity points.”

Fixed points for cyclic orbital generalized contractions on complete metric spaces

Erdal Karapınar, Salvador Romaguera, Kenan Taş (2013)

Open Mathematics

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We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize...

An observation on Kannan mappings

Masato Nakanishi, Tomonari Suzuki (2010)

Open Mathematics

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In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.

Fixed point results on a metric space endowed with a finite number of graphs and applications

Hajer Argoubi, Bessem Samet, Mihai Turinici (2014)

Czechoslovak Mathematical Journal

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In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.