• FIXED POINT THEOREMS FOR MODIFIED F-CONTRACTION MAPPINGS

Abstract

In this paper, we introduce the notion of Modified F-Contraction condition in the non-Archimedean fuzzy metric space, which is a fuzzy version of F-contraction condition of the Hardy-Rozers type in the non-Archimedean fuzzy metric space. Our result generalizes many results of fixed-point theory in the existing literature, specially the results of Wardowski [D.Wardowski, Fixed points of a new type of contractive in complete metric space, Fixed point Theory Appl. 2012,2012,94.], Cosentino and Vetro [V. Cosentino and P. Vetro, Fixed point Result for F-contractive mappings of Hardy-Rogers Type,  Filomat (28)(2014), 715-722] and Piri and Kuman [H. Piri and P. Kuman. Some fixed point theorems concerning F-contraction in complete metric spaces. Fixed point theory Appl. 2014, 21(2014)]. An illustrative example is given to validate our main theorem.