In this paper, we use the de nition of fuzzy normed spaces given byBag and Samanta and provide four types of fuzzy versions of contraction. We show that these mappings necessarily have unique  xed points in fuzzynormed linear spaces. Moreover we prove that the presented theorems areindeed fuzzy extensions of their classical counterparts.

In this present paper, inspired by the concept of weakly Contractive mapping in metric spaces, we introduce the concept of weakly Contractive mapping in generalized asymmetric metric spaces and we establish various fixed point theorems for such mappings in complete generalized metric spaces.

In this paper, two double sequence iterations for a strongly r-Contractive mapping in the modular space are introduced. It is proved that these sequence iterations are strongly convergent to a fixed point of a strongly r-Contractive mapping. Finally, some examples are presented to show the novelty of the main result.

In this paper, the notion of fuzzy $(\theta, \mathcal {L})$-weak contraction in $\mathbb{G}-$metric space is introduced, and sufficient conditions for the existence of fuzzy fixed points for such mappings are investigated. Relevant illustrative examples are constructed to support the assumptions of our established theorems. It is observed that the principal ideas obtained herein extend and subsume some well-known results in the corresponding literature. A few of these special cases of our results are noted and discussed as corollaries

The aim of this paper is to establish certain new classes of proximal contraction mappings and establish some bestproximity point theorems for such kinds of mapping, thereby we extend some fixed point theorems for generalizedweakly Contractive mappings in metric spaces to the case of non-self mapping.

In the present paper, we introduce the notions of ,-type and generalized ,--type multi-valued Contractive mappings in a Menger PbM-space and obtain some new , xed point theorems for both ,-admissible and (, , )-admissible mappings. Our results extensively gen-eralize previous results in this framework. Furthermore, we support our results by some non-trivial examples and an application.