Fixed Points for Nonself Mappings in Metric Spaces

Daiga Grundmane

In this paper we try to extend several well known fixed point theorems for nonself mappings in Banach spaces to mappings in metric spaces. To achieve this goal some additional requirements on convexity in metric spaces are needed. We introduce the notions of MP-convex and NMP-convex metric spaces and obtain several results on existence of fixed points for nonself nonexpansive mappings in NMP-convex metric spaces. In particular, the notion of weakly inward mappings is generalized for mappings in metric spaces and the existence of fixed points is proved for mappings satisfying this condition.