From fuzzy metric spaces to modular metric spaces: a fixed point approach

Volume 10, Issue 2, pp 451--464 http://dx.doi.org/10.22436/jnsa.010.02.11

Publication Date: February 20, 2017 Submission Date: November 07, 2016

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Authors

Fairouz Tchier - Mathematics Department, College of Science (Malaz), King Saud University, P. O. Box 22452, Riyadh, King Saudi Arabia. Calogero Vetro - Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy. Francesca Vetro - Department of Energy, Information Engineering and Mathematical Models (DEIM), University of Palermo, Viale delle Scienze, 90128, Palermo, Italy.

Abstract

We propose an intuitive theorem which uses some concepts of auxiliary functions for establishing existence and uniqueness of the fixed point of a self-mapping. First we work in the setting of fuzzy metric spaces in the sense of George and Veeramani, then we deduce some consequences in modular metric spaces. Finally, a sample homotopy result is derived making use of the main theorem.

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Keywords

• Fixed point
• fuzzy metric space
• modular metric space.

MSC

•  54H25
•  54A40

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