A natural selection of a graphic contraction transformation in fuzzy metric spaces

Volume 11, Issue 2, pp 218--227 http://dx.doi.org/10.22436/jnsa.011.02.04

Publication Date: January 23, 2018 Submission Date: July 02, 2017 Revision Date: November 14, 2017 Accteptance Date: December 08, 2017

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Authors

Hanan Alolaiyan - Department of Mathematics, King Saud University, Saudi Arabia. Naeem Saleem - Department of Mathematics, University of Management and Technology, Lahore, Pakistan. Mujahid Abbas - Department of Mathematics, Government College University, Lahore, Pakistan. - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.

Abstract

In this paper, we study sufficient conditions to find a vertex \(v\) of a graph such that \(Tv\) is a terminal vertex of a path which starts from \(v,\) where \(T\) is a self graphic contraction transformation defined on the set of vertices. Some examples are presented to support the results proved herein. Our results widen the scope of various results in the existing literature.

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Keywords

• Graphic contraction
• fuzzy metric space
• natural selection

MSC

•  47H10
•  47H04
•  47H07
•  54H25
•  54C60

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