Best proximity points in partially ordered metric spaces
Abstract
The existence of best proximity point is an important aspect of optimization theory. We define the concept of proximally monotone Lipschitzian mappings on a partially ordered metric space. Then we obtain sufficient conditions for the existence and uniqueness of best proximity points for these mappings in partially ordered CAT(0) spaces. This work is a continuation of the work of Ran and Reurings [Proc. Amer. Math. Soc. 132 (2004), 1435–1443] and Nieto and Rodr´ ıguez-López [Order, 22 (2005), 223–239] for the new class of mappings introduced herein.
Copyright © 2018 S. A. Shukri, A. R. Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. A. Shukri, A. R. Khan, Best proximity points in partially ordered metric spaces, Adv. Fixed Point Theory 8 (2018), 118–130. https://doi.org/10.28919/afpt/3540
BibTeX
@article{Shukri2018,
author = {Shukri, S. A. and Khan, A. R.},
title = {Best proximity points in partially ordered metric spaces},
journal = {Adv. Fixed Point Theory},
volume = {8},
year = {2018},
pages = {118--130},
doi = {10.28919/afpt/3540}
}