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Common best proximity points theorems in metric spaces

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Abstract

In this paper, we first give an existence and uniqueness common best proximity point theorem for a pair of non-self mappings, one of which weakly dominates the other proximally. Moreover, an algorithm is exhibited to determine such unique common best proximity point. An example is also given to support our main result. Our main result extends and unifies some well-known results in the literature.

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Acknowledgments

The author is grateful to the referees for their helpful comments leading to improvement of the presentation of the work. This research is partially carried out in the IPM-Isfahan Branch. The author was partially supported by the University of Shahrekord, by the Center of Excellence for Mathematics, University of Shahrekord, Iran and by a grant from IPM (No. 91470412).

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Shahrekord, Shahrekord, 88186-34141, Iran

    A. Amini-Harandi

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran

    A. Amini-Harandi

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  1. A. Amini-Harandi
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Correspondence to A. Amini-Harandi.

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Amini-Harandi, A. Common best proximity points theorems in metric spaces. Optim Lett 8, 581–589 (2014). https://doi.org/10.1007/s11590-012-0600-7

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