Conditions of non-empty intersections of closed sets using non-self maps
Abstract
In this paper, we find a set of conditions under which two closed subsets of a metric space have nonempty intersection. We show that the existence of a non-self map from one of the sets to the other satisfying a weak contraction inequality along with some other conditions is sufficient to ensure the nonempty intersection. Further it is shown that the intersection contains the unique fixed point of the mapping. The result has a corollary and is illustrated with two examples. One of the examples show that the main theorem properly contains its corollary.
Copyright © 2013 Binayak S. Choudhury, Pranati Maity. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
B. S. Choudhury, P. Maity, Conditions of non-empty intersections of closed sets using non-self maps, Adv. Fixed Point Theory 4 (2014), 91–101.
BibTeX
@article{Choudhury2014,
author = {Choudhury, Binayak S. and Maity, Pranati},
title = {Conditions of non-empty intersections of closed sets using non-self maps},
journal = {Adv. Fixed Point Theory},
volume = {4},
year = {2014},
pages = {91--101},
doi = {}
}