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On coupled best proximity points and Ulam–Hyers stability

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Abstract

For two nonempty, closed, bounded and convex subsets A and B of a uniformly convex Banach space X consider a mapping \(T:(A \times B) \cup (B \times A) \rightarrow A \cup B\) satisfying \(T(A,B) \subset B\) and \(T(B, A) \subset A\). In this paper the existence of a coupled best proximity point is established when T is considered to be a p-cyclic contraction mapping and a p-cyclic nonexpansive mapping. The Ulam–Hyers stability of the best proximity point problem is also studied. Moreover, we establish the existence of a solution of the bi-equilibrium problem in Hilbert spaces as an application.

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Acknowledgements

The authors are grateful to the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Netaji Nagar, New Delhi, 110023, India

    Anuradha Gupta

  2. Department of Mathematics, University of Delhi, New Delhi, 110007, India

    Manu Rohilla

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  1. Anuradha Gupta
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  2. Manu Rohilla
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Correspondence to Manu Rohilla.

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The corresponding author is supported by University Grants Commission Research Grant (Ref.No. NFO-2018-19-OBC-HAR-72140).

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Gupta, A., Rohilla, M. On coupled best proximity points and Ulam–Hyers stability. J. Fixed Point Theory Appl. 22, 28 (2020). https://doi.org/10.1007/s11784-020-0764-1

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  • DOI: https://doi.org/10.1007/s11784-020-0764-1

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