On the Conditions of Fixed-Point Theorems Concerning F-Contractions

We prove a fixed-point theorem that generalizes and simplifies a number of results in the theory of F-contractions. We show that all of the previously imposed conditions on the operator can be either omitted or relaxed. Furthermore, our result is formulated in the more general context of b-metric spaces and phi-contractions. We also point out that the framework of F-contractions can be reformulated in an equivalent way that is both closer in spirit to the classical syntax of Banach-type fixed point theorems, and also more natural and easier to deal with in the proofs.