A New Study on Common Fixed Points for ($α$-$β$-$F$)-Contraction Mappings

Abstract

This paper explores the existence of common fixed points for a newly introduced class of mappings called ($α$-$β$-$F$)-contraction mappings in metric spaces. We establish several common fixed point theorems under specific conditions, incorporating ($α$-$β$-$F$)-weak contractions to extend and generalize existing results in fixed point theory. Unlike many classical approaches, our framework retains flexibility while accommodating key structural properties such as compactness and continuity. To support the theoretical findings, illustrative examples are provided. These results enhance the understanding and applicability of fixed point theory.