Best proximity points in partially ordered metric spaces
Advances in Fixed Point Theory · 2018
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.