Remarks on the paper "Best proximity point theorem in higher dimensions with an application"

Document Type : Research Paper

Authors

1 Department of Mathematics, School of Basic and Applied Sciences, Adamas University, Barasat-700126, India

2 Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

Abstract

Very recently S. Mondal et al. [Best proximity point theorem in higher dimensions with an application, Int. J. Nonlinear Anal. Appl. (2022) ] introduced the concept of $F_n$-contractions ($n\geq 2$) and investigated the existence and uniqueness of an $n$-tuple best proximity point for this class of mappings in the framework of metric spaces. In this paper, we prove that their main result is a straightforward consequence of the Banach contraction principle.

Keywords

[1] S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrals, Fund. Math. 3 (1922), 133—181.
[2] M. Gabeleh, Global optimal solutions of non-self mappings, Sci. Bull.‘Politeh.’Univ. Buchar. Ser. A. 75 (2013), 67–74.
[3] M. Gabeleh and O.O. Otafudu, Markov–Kakutani’s theorem for best proximity pairs in Hadamard spaces, Indag. Math. 28 (2017), 680–693.
[4] S. Mondal, S. Lahal and A. Chanda, Best proximity point theorem in higher dimensions with an application, Int. J. Nonlinear Anal. Appl. 13 (2022), no. Special Issu, 97–10
Volume 14, Issue 4
April 2023
Pages 333-336
  • Receive Date: 14 June 2022
  • Revise Date: 30 June 2022
  • Accept Date: 19 August 2022
  • First Publish Date: 27 August 2022