Abstract
In the year 2012, Caballero et al. [Fixed Point Theory Appl. 2012:231 (2012)] introduced the notion of Geraghty-contraction for non-self mappings and studied the existence and uniqueness of best proximity point for this class of mappings to generalize the fixed point result due to Geraghty. In this short note, we show that the existence of best proximity point for Geraghty-contraction follows from fixed point theorem 2.1 of Geraghty [Proc. Amer. Math. Soc. 40 (2) 604–608 (1973)] i.e., the existence of best proximity point for Geraghty-contraction follows from the same conclusion in fixed point theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banach, S. 1922. Sur les operations dans les ensembles abstraits et leur applications aux equations integrals. Fund. Math. 3: 133–181.
Bucur, A. 2017. About applications of the fixed point theory. Sci. Bull. 22 (1):13–17. https://doi.org/10.1515/bsaft-2017-0002.
Caballero, J., J. Harjani, and K. Sadarangani. 2012. A best proximity point theorem for Geraghty-contractions. Fixed Point Theory Appl. 2012: 231. https://doi.org/10.1186/1687-1812-2012-231.
Geraghty, M.A. 1973. On contractive mappings proc. Amer. Math. Soc. 40 (2): 604–608.
Acknowledgements
We like to thank the learned referees for his/her careful reading and constructive suggestions which undoubtedly improve the presentation as well as the depth of the paper.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
Author of this paper declares that he has no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by Samy Ponnusamy.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Som, S. A remark on the paper “A best proximity point theorem for Geraghty-contractions”. J Anal 30, 959–963 (2022). https://doi.org/10.1007/s41478-022-00383-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41478-022-00383-4