Some results on fuzzy metric space and some examples of fuzzy b-metric space

Abstract

ABSTRACT. The problem of constructing a satisfactory theory of fuzzy metric spaces has been investigated by several researchers from different point of view. The concept of fuzzy sets was introduced by Zadeh. Following fuzzy metric space and fuzzy b−metric space modified by Kramosil, Mickalek-George and Veeramani using continuous triangular norm. A binary operation ∗ : [0, 1] × [0, 1] → [0, 1] is a continuous triangular norm t-norm, if ∗ is associative, com mutative, continuity, monotonicity and 1 acts as identity element. Some typi cal examples of t−norm are product t−norm, minimum t−norm, lukasiewitz t− norm and hamacher t−norm. In our work we used minimum triangu lar t−norm and Banach fixed point theorem to prove fixed point theorem in Fuzzy metric space and discuss some examples of Fuzzy b−metric space. Let ting (X, M, ∗) be a complete fuzzy metric space and T : X → X is a continuous function satisfying the condition