Conditions of non-empty intersections of closed sets using non-self maps

Binayak S. Choudhury, Pranati Maity

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.

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How to Cite this Article:

Binayak S. Choudhury, Pranati Maity, Conditions of non-empty intersections of closed sets using non-self maps, Advances in Fixed Point Theory, Vol 4, No 1 (2014), 91-101

Copyright © 2014 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.

Advances in Fixed Point Theory

ISSN: 1927-6303

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