A Generalization of a Theorem of Móricz and Rhoades on Weighted Means

In this paper,we prove a theorem which gives an equivalent formulation of summability by weighted mean methods. The result of Hardy [1] and that of Móricz and Rhoades [2] are special cases of this theorem. In this context, it is important to note that the result of Móricz and Rhoades is valid even without the assumption $\frac{p_n}{P_n}\to 0$ as $n\to \mathrm{\infty }$.