Abstract
Suppose that A and B are nonempty subsets of a complete metric space \((\mathcal {M},d)\) and \(\phi ,\psi :A\rightarrow B\) are mappings. The aim of this work is to investigate some conditions on \(\phi \) and \(\psi \) such that the two functions, one that assigns to each \(x\in A\) exactly \(d(x,\phi x)\) and the other that assigns to each \(x\in A\) exactly \(d(x,\psi x)\), attain the global minimum value at the same point in A. We have introduced the notion of proximally F-weakly dominated pair of mappings and proved two theorems that guarantee the existence of such a point. Our work is an improvement of earlier work in this direction. We have also provided examples in which our results are applicable, but the earlier results are not applicable.
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Acknowledgements
As a Ph.D. student, the first author is grateful to University of Delhi and Government of India for awarding him with a Non N.E.T. fellowship. We would like to thank anonymous reviewers for taking the time and effort to review the manuscript and providing helpful suggestions, which has greatly improved it.
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The first author is receiving a Non N.E.T. fellowship from University of Delhi.
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Communicated by S Ponnusamy.
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Deep, A., Batra, R. Common best proximity point theorems under proximal F-weak dominance in complete metric spaces. J Anal 31, 2513–2529 (2023). https://doi.org/10.1007/s41478-023-00570-x
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DOI: https://doi.org/10.1007/s41478-023-00570-x