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In this paper 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 signiflcantly 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.

On the solution of Steinhaus functional equation using weakly Picard operators