contractive type mapping

In this paper‎, ‎we present innovative concepts of fuzzy type contractions and leverage them to establish fixed point theorems for fuzzy mappings within the framework of fuzzy metric spaces‎. ‎The results of this article are applied to multivalued mappings and fuzzy mappings for contractive fuzzy type mappings‎. ‎Through illustrative examples‎, ‎we showcase the practical applicability of our proposed notions and results‎, ‎demonstrating their effectiveness in real-world scenarios‎.

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

In the present paper, we introduce new types of convergence of a sequence in left dislocated and right dislocated metric spaces. Also, we generalize Banach contraction principle in these newly defined generalized metric spaces.

In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illustrative examples are also given to substantiate our newly proved results.