Common best proximity results for multivalued proximal contractions in metric space with applications
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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.
Share and Cite
ISRP Style
Nawab Hussain, Abdul Rahim Khan, Iram Iqbal, Common best proximity results for multivalued proximal contractions in metric space with applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4814--4828
AMA Style
Hussain Nawab, Khan Abdul Rahim, Iqbal Iram, Common best proximity results for multivalued proximal contractions in metric space with applications. J. Nonlinear Sci. Appl. (2016); 9(6):4814--4828
Chicago/Turabian Style
Hussain, Nawab, Khan, Abdul Rahim, Iqbal, Iram. "Common best proximity results for multivalued proximal contractions in metric space with applications." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4814--4828
Keywords
- \(\alpha_*\)-proximal admissible mapping
- common best proximity point
- multivalued mapping.
MSC
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