Stability of Certain Functional Equations Via a Fixed Point of ĆiriĆ

Mohamed Akkouchi

Let $S$ be a non empty set. We prove the stability (in the sense of Ulam) of the functional equation: $f(t)=F(t,f(\phi(t)))$, where $\phi$ is a given function of $S$ into itself and $F$ is a function satisfying a contraction of \'Ciri\'c type [5]. Our analysis is based on the use of a fixed point theorem of \'Ciri\'c (see [5] and [4]). In particular our result provides a generalization and a natural continuation of a paper of Baker [3].