Hybrid fixed point in CAT(0) spaces

Abstract

In this paper, we introduce an ultrapower approach to prove fixed point theorems for $H^{+}$-nonexpansive multi-valued mappings in the setting of CAT(0) spaces and prove several hybrid fixed point results in CAT(0) spaces for families of single-valued nonexpansive or quasinonexpansive mappings and multi-valued upper semicontinuous, almost lower semicontinuous or $H^{+}$-nonexpansive mappings which are weakly commuting. We also establish a result about structure of the set of fixed points of $H^{+}$-quasinonexpansive mapping on a CAT(0) space.