International Journal of Nonlinear Analysis and Applications

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
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 4
April 2023
Pages 333-336
  • Receive Date: 14 June 2022
  • Revise Date: 30 June 2022
  • Accept Date: 19 August 2022