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In this paper, we introduce the notions of fuzzy a-Geraghty contraction type mapping and fuzzy a-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known comparable results in the literature. Furthermore, several illustrative examples are given to support the usability of our obtained results. [ABSTRACT FROM AUTHOR]

We consider the concept of fuzzy quasi-contractions initiated by Ćirić in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy H-contractive mappings on M-complete fuzzy metric spaces in the sense of George and Veeramani. The results are illustrated by a representative example. [ABSTRACT FROM AUTHOR]

Recently, Phiangsungnoen et al. [J. Inequal. Appl. 2014:201 (2014)] studied fuzzy mappings in the framework of Hausdorff fuzzy metric spaces. Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. Finally, as an application of our results, we investigate the existence of solution for some recurrence relations associated to the analysis of quicksort algorithms. [ABSTRACT FROM AUTHOR]

In the present paper, we give a new approach to Caristi's fixed point theorem on non-Archimedean fuzzy metric spaces. For this we define an ordinary metric d using the non-Archimedean fuzzy metric M on a nonempty set X and we establish some relationship between (X, d) and (X, M, *). Hence, we prove our result by considering the original Caristi's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, the concept of fuzzy metric-like spaces is introduced which generalizes the notion of fuzzy metric spaces given by George and Veeramani [8]. Some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of our new results where result from current literature are not applicable. [ABSTRACT FROM AUTHOR]

The sequential p-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called s-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are s-convergent. In such a case M is called an s-fuzzy metric. If (NM,*) is a fuzzy metric on X where NM(x,y) = Λ{M(x, y, t) : t > 0} then it is proved that the topologies deduced from M and NM coincide if and only if M is an s-fuzzy metric. [ABSTRACT FROM AUTHOR]

Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154- 2165], we introduce the notions of α-Φ-fuzzy contractive mapping and β-ψ-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of fuzzy generalized contraction and give a fixed point result for such mappings in the setting of fuzzy M-complete metric spaces. We also give an affirmative partial answer to a question posed by Wardowski [D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces. Fuzzy Set Syst., 222(2013), 108-114]. Some examples are also given to support our main result. [ABSTRACT FROM AUTHOR]

We obtain two fixed point theorems for a kind of ᵩ-contractions in complete fuzzy metric spaces, which are applied to easily deduce intuitionistic versions that improve and simplify the recent results of X. Huang, C. Zhu and X. Wen. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified intuitionistic fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

In a fuzzy metric space (X, M, *), where * is a continuous t--norm, a locally fuzzy contraction mapping is defined. It is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. Also, if f satisfies the locally fuzzy contractivity condition then it satisfies the global fuzzy contractivity condition. [ABSTRACT FROM AUTHOR]

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Banach's contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiec's sense. We show here that this is not the case, for which we present an example of a compact fuzzy metric space that is not complete in Grabiec's sense. On the other hand, Grabiec used a notion of compactness to obtain a fuzzy version of Edelstein's contraction principle. We present here a generalized version of Grabiec's version of the Edelstein fixed point theorem and different interesting facts on the topology of fuzzy metric spaces. [ABSTRACT FROM AUTHOR]