Fixed point-type results for a class of extended cyclic self-mappings under three general weak contractive conditions of rational type

Abstract

This article discusses three weak φ-contractive conditions of rational type for a class of 2-cyclic self-mappings defined on the union of two non-empty subsets of a metric space to itself. If the space is uniformly convex and the subsets are non-empty, closed, and convex, then the iterates of points obtained through the self-mapping converge to unique best proximity points in each of the subsets. © 2011 De la Sen and Agarwal; licensee Springer.