In this paper, we introduce a new fuzzy metric based on gradual numbers. Firstly, the concept of gradual metric spaces is introduced. And then, basic topological concepts in gradual metric spaces are presented and their properties are investigated. Mathematics Subject Classification: 54E35, 03E72

The present paper is mainly concerned with several new types of fixed point theorems in different spaces such as cone metric spaces and fuzzy metric spaces. By using these obtained fixed point theorems, we then prove the existence and uniqueness of the solutions to two classes of two-point ordinary differential equation problems.

In this paper we give a fixed-point theorem for fuzzy contractive mappings in the George and Veeramani p-complete fuzzy metric spaces.

In this paper, we give some new coupled common fixed point theorems for probabilistic φ-contractions in Menger probabilistic metric spaces. As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improve the corresponding results given by some authors. Finally, we give one example to i...

and Applied Analysis 3 Conversely, if the pair of functions α and β satisfy the conditions 1 – 4 , then there exists a unique u ∈ E1 such that u λ α− λ , β λ for each λ ∈ 0, 1 , 9 . The fuzzy number u corresponding to the pair of functions α and β is defined by u : R → 0, 1 , u x sup{λ : α x ≤ λ ≤ β x }, 5 . A sequence u uk of fuzzy numbers is a function u from the set N, the set of all positiv...

In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of completegeneralized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergentmatrix technique with Schauder fixed point princi...

The purpose of this paper is to present some coincidence point and common  fixed point theorems for multivalued contraction maps in complete fuzzy  metric spaces endowed with a partial order. As an application, we give  an existence theorem of solution for general classes of integral  inclusions by the coincidence point theorem.

INTRODUCTION The concept of fuzzy sets introduced by Zadeh [19], was the foundation of fuzzy metric space. Fuzzy metric spaces have been introduced by Kramosil and Michalek [8] and George and Veeramani [3] modified the notion of fuzzy metric spaces with the help of continuous tnorm. Recently many authors such as [4], [7], [14] and [15] have proved fixed point theorems involving fuzzy sets. Bouh...

There are a lot of fixed and common fixed point results in different types of spaces. For example, metric spaces, fuzzy metric spaces, and uniform spaces. One of the most interesting is partial metric space, which is defined by Matthews 1 . In partial metric spaces, the distance of a point in the self may not be zero. After the definition of partial metric space, Matthews proved the partial met...