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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 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.doi:10.2298/fil1101069b fatcat:6y2jpgbiyffjxi4lvc2wijajiu