Journal of Nonlinear Analysis and Application

Volume 2018, No. 1 (2018), Pages 57-63

Article ID jnaa-00376, 7 Pages

doi: 10.5899/2018/jnaa-00376


Research Article


Best Proximity Points of Contractive-type and Nonexpansive-type Mappings


R. Kavitha1 *, S. Somasundaram1


1Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, India.


* Corresponding author. Email address: smartkavi89@gmail.com


Received: 23 February 2017; Accepted: 15 March 2017


Copyright © 2018 R. Kavitha and S. Somasundaram. 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

The purpose of this paper is to obtain best proximity point theorems for multivalued nonexpansive-type and contractive-type mappings on complete metric spaces and on certain closed convex subsets of Banach spaces. We obtain a convergence result under some assumptions and we prove the existence of common best proximity points for a sequence of multivalued contractive-type mappings.


Keywords: Best proximity point; Contractive-type and nonexpansive-type multivalued maps; Common best proximity point.


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