Uniqueness of fixed points for sums of operators in ordered Banach spaces and applications

Abstract

In this article, we are concerned by existence and uniqueness of a fixed point for the sum of two operators A and B, defined on a closed convex subset of an ordered Banach space, where the order is induced by a normal and minihedral cone. In such a structure, an absolute value function is generated by the order and this provide the ability to introduce new versions of the concepts of lipschitzian and expansive mappings. Therefore we prove that if A is expansive and B is contractive, then the sum A + B has a unique fixed point.