On monotone nonexpansive mappings in CAT p ( 0 ) $\operatorname{CAT}_{p}(0)$ spaces

Abstract

Abstract In this paper, based on some geometrical properties of CAT p ( 0 ) $\operatorname{CAT}_{p}(0)$ spaces, for p ≥ 2 $p \geq 2$ , we obtain two fixed point results for monotone multivalued nonexpansive mappings and proximally monotone nonexpansive mappings. Which under some assumptions, reduce to coincide and generalize a fixed point result for monotone nonexpansive mappings. This work is a continuity of the previous work of Ran and Reurings, Nieto and Rodríguez-López done for monotone contraction mappings.

Keywords

• Fixed points
• Best proximity points
• CAT p ( 0 ) $\operatorname{CAT}_{p}(0)$ spaces
• Partial order
• Contraction mappings
• Nonexpansive mappings