On pseudocontractions in cyclic maps
Functional Analysis
2012-08-06 v1
Abstract
This paper discusses a more general contractive condition for a class of extended 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 non-empty, 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.
Keywords
Cite
@article{arxiv.1208.0758,
title = {On pseudocontractions in cyclic maps},
author = {M. De la Sen},
journal= {arXiv preprint arXiv:1208.0758},
year = {2012}
}