On the Solution of Steinhaus Functional Equation Using Weakly Picard Operators

Vasile Berinde

We obtain existence results regarding the solutions $g$ of a Steinhaus type functional equation of the form $g(x)+g(f(x))=F(x)$, under the significantly weaker assumption that $f$ is a weakly Picard operator. The solutions are given in terms of sums of either convergent series or divergent series but summable by some method of summability.