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

Document Type : Research Paper

Authors
Sumit Som 1
Moosa Gabeleh 2
1 Department of Mathematics, School of Basic and Applied Sciences, Adamas University, Barasat-700126, India
2 Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
10.22075/ijnaa.2022.27496.3623
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
Best proximity point
$F_n$-contraction
weak $P$-property
$n$-tupled fixed point
$n$-tupled best proximity point
[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

Article View 17,496
PDF Download 10,499