ON COUPLED FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE

Abstract

The study of coupled fixed points of nonlinear operators, which was introduced about three decades ago, got a boost in 2006 when Bhaskar and Lakshmikantham (2006) studied the coupled fixed points of some contractive maps in partially ordered metric spaces and applied it to solve some first-order ordinary differential equations with periodic boundary problems. Since then, coupled fixed points theorems have been proved by several authors for certain contractive maps in both partially ordered and cone metric spaces. The study of coupled fixed point, previously limited to quasi-contractive maps, was recently extended to asymptotically nonexpansive mappings in uniformly convex Banach spaces by Olaoluwa, Olaleru, and Chang (2013). In this paper, their results (demiclosed principle and existence result) are extended to asymptotically nonexpansive maps in the intermediate sense in a wider class of spaces. The study naturally opens up new areas of research on the study of coupled fixed points of different classes of pseudocontractive maps.