A Nonlinear Fuzzy Contraction Principle via Control Functions

Abstract

In this work, we develop a new type of nonlinear fuzzy contraction, namely fuzzy $\mathcal{L}_{\lambda}$-weak contraction, based on fuzzy $\mathcal{L}_{\lambda}$-simulation function and fuzzy $\Theta_{f}$-contractive mappings. Then, using the specifically developed contraction, we show the existence and uniqueness of a fixed point for a self-mapping in complete fuzzy metric spaces. We provide an example, together with some illustrative corollaries and remarks, to further prove the validity of our findings.
The presented findings combine, enhance, and extend a number of earlier research findings.