Fixed Point Theorems in Neutrosophic Fuzzy Metric Space and a Characterization to its Completeness

Abstract

The present research work aims to establish some basic conventional fixed point theorems such as the Banach fixed point theorem, Edelstein fixed point theorem and Kannan fixed point theorem, for a recently introduced topological space, known as the neutrosophic fuzzy metric space. The Kannan fixed point theorem has also further been classified into two categories namely, (1/2)−Kannan and (1)−Kannan fixed point theorems. Also the concept of semi-metric in the said space has been introduced, and along with it the results hence obtained are used to characterize the completeness of the mentioned space. To the best of known literatures, this type of work in the said space has not yet been found.

Keywords

• fixed point (fp)
• fuzzy sets (fs)
• fuzzy metric space (fms)
• neutrosophic sets (ns)
• neutrosophic fuzzy sets (nfs)
• neutrosophic fuzzy metric space (nfms)
• kannan contraction (kc)