Generalized nonexpansive mappings in ordered metric spaces and their (common) fixed points with applications

Abstract

We introduce a generalized nonexpansive condition for a map in an ordered metric space and derive fixed point theorems for a nondecreasing mapping. Moreover, common fixed point results are obtained for a pair of mappings satisfying an appropriate nonexpansive condition. To illustrate our results, we give throughout the paper some examples. Applications of the obtained results to integral equations and first-order periodic boundary value problems are presented. © 2013 Springer-Verlag Italia.