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

Natarajan P.N.

Commentationes Mathematicae

2012

Vol. 52, [Z] 1

29-37

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 Pn/Pn→ 0 as n→∞.

Another Theorem on Weighted Means

Natarajan P.N.

Commentationes Mathematicae

2010

Vol. 50, [Z] 2

175-181

In this short paper, which is a continuation of [2], we prove another interesting result concerning weighted means.