M. Mandal - Department of Mathematics, School of Basic and Applied Sciences, Adamas University, Barasat-700126, India. S. Som - Department of Mathematics, School of Basic and Applied Sciences, Adamas University, Barasat-700126, India. - Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Madhya Pradesh-466114, India.
In the year 2016, Pragadeeswarar et al. [V. Pragadeeswarar, M. Marudai, P. Kumam, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 1911--1921] considered a special class of multi-valued mappings and investigated the existence of best proximity points for such class of mappings which generalizes the fixed point result established by Choudhury et al. [B. S. Choudhury, N. Metiya, Arab J. Math. Sci., \({\bf 17}\) (2011), 135--151] in the context of partially ordered metric spaces. In this note, we have showed that the best proximity point result is a direct consequence of the corresponding fixed point result. In the last part of this note, we applied our result in [V. Pragadeeswarar, M. Marudai, P. Kumam, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 1911--1921, Example 2.2] to validate our claim.
M. Mandal, S. Som, Equivalence between best proximity point and fixed point for some class of multi-valued mappings, Journal of Nonlinear Sciences and Applications, 17 (2024), no. 3, 123--127
Mandal M., Som S., Equivalence between best proximity point and fixed point for some class of multi-valued mappings. J. Nonlinear Sci. Appl. (2024); 17(3):123--127
Mandal, M., Som, S.. "Equivalence between best proximity point and fixed point for some class of multi-valued mappings." Journal of Nonlinear Sciences and Applications, 17, no. 3 (2024): 123--127
