Fixed Point Theorems for Single valued mapping and Set Valued Mapping in Fuzzy Metric spaces through

Abstract

Fuzzy metric spaces are an extension of classical metric spaces that incorporate the concept of fuzziness
into the measurement of distance. It provides a flexible framework for analyzing situations where
precision is not feasible or desirable. It offers valuable insights in areas requiring the handling of vague or
imprecise information, broadening the scope of traditional mathematical analysis. The present
manuscript deals with establishment of fixed point and  -fuzzy fixed point theorems for Single valued
mapping and Set Valued Mapping in Fuzzy Metric spaces through  -admissible approach, which is an
extension and generalization of the results of many authors with new rational contractive conditions.
Established results are generalizations of previous known results in the field of fixed point theory
concerning to fuzzy metric spaces.