Common best proximity results for multivalued proximal contractions in metric space with applications

Volume 9, Issue 6, pp 4814--4828 http://dx.doi.org/10.22436/jnsa.009.06.117

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Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Abdul Rahim Khan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia. Iram Iqbal - Department of Mathematics, University of Sargodha, Sargodha, Pakistan.

Abstract

The study of the best proximity points is an interesting topic of optimization theory. We introduce the notion of \(\alpha_*\)-proximal contractions for multivalued mappings on a complete metric space and establish the existence of common best proximity point for these mappings in the context of multivalued and single-valued mappings. As an application, we derive some best proximity point and fixed point results for multivalued and single-valued mappings on partially ordered metric spaces. Our results generalize and extend many known results in the literature. Some examples are provided to illustrate the results obtained herein.

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Keywords

• \(\alpha_*\)-proximal admissible mapping
• common best proximity point
• multivalued mapping.

MSC

•  47H10
•  46N40
•  54H25
•  46T99

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