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Journal of Mathematics
Volume 2015, Article ID 302012, 4 pages
http://dx.doi.org/10.1155/2015/302012
Research Article

Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India

Received 29 July 2015; Revised 8 September 2015; Accepted 13 September 2015

Academic Editor: Alfred Peris

Copyright © 2015 Binayak S. Choudhury and Chaitali Bandyopadhyay. 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.

Abstract

We consider a problem of stability of fixed point sets for a sequence of multivalued mappings defined on a metric space converging to a limit function where the convergence is with respect to the Pompeiu-Hausdorff distance. The members of the sequence are assumed to be multivalued almost contractions. We show that the fixed point sets of this sequence of mappings are stable.