Fixed points of mappings satisfying implicit $F$-contractive conditions

Abstract

This paper presents a generalized fixed point theorem in metric spaces or ordered metric spaces using an implicit relation to unify various $F$-contractive type mappings. Relying only on the strict monotonicity of the auxiliary function $F$, the result extends previous work and includes corollaries that demonstrate its generality. The approach simplifies the analysis by eliminating the need for separate proofs for each type of contraction.