New Fixed Point Results for (τ -k)-F-Contraction Mappings in Complete Metric Spaces

Abstract

In this paper, we introduce and study two novel classes of contractions in complete metric spaces, namely the (τ , k)-F-contractions and (τ , k)-F-weak contractions. These notions generalize and unify several well-known contraction conditions in the existing literature. We establish sufficient conditions ensuring the existence and uniqueness of fixed points for such mappings in complete metric spaces. In addition, illustrative examples are presented to verify the applicability and effectiveness of the proposed results. The findings of this work extend and enhance many classical fixed point theorems within the framework of metric spaces.