Best proximity points of discontinuous operator in partially ordered metric spaces

Volume 10, Issue 1, pp 308--315 http://dx.doi.org/10.22436/jnsa.010.01.29

Publication Date: January 27, 2017 Submission Date: September 06, 2016

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Authors

B. S. Choudhury - Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India. M. Jleli - Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia. P. Maity - Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India.

Abstract

In this paper we establish best proximity point results for monotone multivalued mappings in partially ordered metric spaces. We consider three notions of monotonicity of multivalued mappings. The main theorem is obtained by utilizing property UC and MT-functions. There is no requirement of continuity on the multivalued function which is illustrated with two supporting examples of the results established in this paper. There are two corollaries. Some existing results are extended to the domain of partially ordered metric spaces through one of the corollaries.

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Keywords

• Best proximity point
• multivalued cyclic mapping
• multivalued approximately monotone increasing mapping
• multivalued partly monotone increasing mapping.

MSC

•  54H10
•  54H25
•  47H10

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