Abstract. We generalize a theorem pertaining to the factorization of inequalities of infinite series. The generalization means that we replace the function $x^p$, playing a crucial role in the antecedent theorem, by a more general function $\varphi(x)$.

AMS Subject Classification (1991): 26D15, 40D09

Received November 25, 1998 and in revised form December 9, 1998. (Registered under 2674/2009.)