Some fixed point-type results for a class of extended cyclic self-mappings with a more general contractive condition

Abstract

This article discusses a more general contractive condition for a class of extended (p ≥ 2) -cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. If the space is uniformly convex and the subsets are nonempty, closed and convex, then all the iterates converge to a unique closed limiting finite sequence which contains the best proximity points of adjacent subsets and reduces to a unique fixed point if all such subsets intersect. © 2011 De la Sen and Agarwal; licensee Springer.