Global best approximate solutions for set-valued cyclic \(\alpha\)-\(F\)-contractions

Volume 10, Issue 9, pp 5090--5107 http://dx.doi.org/10.22436/jnsa.010.09.45

Publication Date: September 30, 2017 Submission Date: May 13, 2017

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Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Iram Iqbal - Department of Mathematics, University of Sargodha, Sargodha, Pakistan.

Abstract

In this paper, we introduce the concepts of multivalued cyclic \(\alpha\)-\(F\) contraction and triangular \(\alpha\)-orbital admissible mappings. We use these concepts to find global best approximation solutions in a metric space with proximally complete property. We also provide some nontrivial examples to support our results. As an application, we obtain best proximity point results in partially ordered metric spaces and best proximity point theorems for single-valued mappings. We also prove fixed point results for multivalued and single-valued \(\alpha\)-type \(F\)-contractions.

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Keywords

• Proximally complete pair
• cyclic \(\alpha\)-\(F\)-contraction
• cyclical Cauchy sequence
• best proximity point

MSC

•  46N40
•  47H10
•  54H25
•  46T99

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