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

• Autorzy: Natarajan P.N.
• Języki publikacji: EN

Abstrakty

EN

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→∞.

Słowa kluczowe

EN

regular matrix; weighted means; equivalence

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2012
• Tom: Vol. 52, [Z] 1
• Strony: 29--37
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Natarajan P.N.

• Old No. 2/3, New No. 3/3, Second Main Road, R.A. Puram, Chennai 600 028, India,

Bibliografia

• [1] G.H. Hardy, A theorem concerning summable series, Proc. Cambridge Philos. Soc. 20 (1920-21), 304-307.
• [2] F. Móricz and B.E. Rhoades, An equivalent reformulation of summability by weighted mean methods, revised, Linear Algebra Appl. 349 (2002), 187-192.
• [3] A. Peyerimhoff, Lectures on summability, Lecture Notes in Mathematics 107, Springer, 1969.