  We prove a fixed-point theorem that generalises 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 $\varphi$-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.
