On the solution of Steinhaus functional equation using weakly Picard operators

Vasile Berinde
2011 Filomat  
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