In this paper, we introduce a new class of control functions, namely extended $\mathcal{FZ}$ FZ -simulation functions, and employ it to define a new contractive condition. We also prove some new fixed and best proximity point results in the context of an M-complete fuzzy metric space. The presented theorems unify, generalize, and improve several existing results in the literature.

In this paper, we introduce a new concept of α-admissible almost type Z-contraction and prove some fixed point results for this new class of contractions in the context of complete metric spaces. The presented results generalize and unify several existing results in the literature.

In this study, we introduce new concepts of α − FZ -contraction and α − ψ − FZ -contraction and we discuss existence results of the best proximity points of such types of non-self-mappings involving control functions in the structure of complete fuzzy metric spaces. Our results extend, generalize, enrich, and improve diverse existing results in the current literature.

In this paper, we introduce two new concepts, generalized α-η-FZ-contraction and modified α-η-FZ-contraction, which unify several types of contractions in the context of fuzzy metric spaces. We discuss the existence and uniqueness results of such mappings in the setting of a complete fuzzy metric space in the sense of George and Veeramani and present several significant consequences of our obtained results by using variant examples for FZ-simulation functions and admissible mappings. Some examples are provided to illustrate the usability of our main results.

No abstract