Contraction Mapping Theorem in Partial Fuzzy Metric Spaces

Abstract

The contraction mapping theorem and its application are often encountered in 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 is defined using fuzzy points.

Keywords

• partial fuzzy metric space
• contraction mapping theorem
• fuzzy points
• contraction mapping