Contraction Mapping Theorem in Partial Fuzzy Metric Spaces

Fadhel S. Fadhel; Jaafer Hmood Eidi; Hazim M. Wali

doi:10.6180/jase.202204_25(2).0020

Contraction Mapping Theorem in Partial Fuzzy Metric Spaces

Fadhel S. Fadhel ¹, Jaafer Hmood Eidi², and Hazim M.Wali²

¹Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, Iraq
²Department of Mathematics, College of Education, Al-Mustansiriyah University, Baghdad, Iraq

Received: July 9, 2021
Accepted: September 6, 2021
Publication Date: September 29, 2021

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202204_25(2).0020

ABSTRACT

Contraction mapping theorem and its application is often encountered different fields of pure and applied mathematics. In this work, three aims are achieved, which are first of introducing and presenting the basic and fundamental necessary concepts for partial fuzzy metric spaces. The second aim is to state and prove two fuzzy contraction mapping theorems in fuzzy partial metric spaces based on the contractive mapping theorem by using the suggested metric function that is defined over fuzzy points rather than fuzzy sets. Also, we present in this paper, as the third aim, the relationship between the usual distance function defined in fuzzy metric spaces and the distance function defined over partial metric space, which are defined using fuzzy points.

Keywords: Partial fuzzy metric space, Contraction mapping theorem, Fuzzy points, Contraction mapping

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