A new note on generalized absolute matrix summability
9 pages

Découvre YouScribe en t'inscrivant gratuitement

Je m'inscris

A new note on generalized absolute matrix summability

-

Découvre YouScribe en t'inscrivant gratuitement

Je m'inscris
Obtenez un accès à la bibliothèque pour le consulter en ligne
En savoir plus
9 pages
Obtenez un accès à la bibliothèque pour le consulter en ligne
En savoir plus

Description

This paper gives necessary and sufficient conditions in order that a series ∑ a n λ n should be summable | B | k , k ≥ 1 , whenever ∑ a n is summable | A | . Some new results have also been obtained. MSC: 40D25, 40F05, 40G99. This paper gives necessary and sufficient conditions in order that a series ∑ a n λ n should be summable | B | k , k ≥ 1 , whenever ∑ a n is summable | A | . Some new results have also been obtained. MSC: 40D25, 40F05, 40G99.

Sujets

Informations

Publié par
Publié le 01 janvier 2012
Nombre de lectures 22

Extrait

Özarslan and AriJournal of Inequalities and Applications2012,2012:166 http://www.journalofinequalitiesandapplications.com/content/2012/1/166
R E S E A R C H
Open Access
A new note on generalized absolute matrix summability * HS Özarslanand T Ari
* Correspondence: seyhan@erciyes.edu.tr Department of Mathematics, Erciyes University, Kayseri, 38039, Turkey
Abstract This paper gives necessary and sufficient conditions in order that a seriesanλn should be summable|B|k,k1, wheneveranis summable|A|. Some new results have also been obtained. MSC:40D25; 40F05; 40G99 Keywords:summability factors; absolute matrix summability; infinite series
1 Introduction Letanbe a given infinite series with the partial sums (sn). Let (pn) be a sequence of positive numbers such that
n Pn=pv→ ∞as (n→ ∞), v=
(Pi=pi= ,i).
The sequence-to-sequence transformation
n tn=pvsv Pn v=
()
()
defines the sequence (tn) of the Riesz means of the sequence (sn) generated by the se-quence of coefficients (pn) (see []). The seriesanis said to be summable|R,pn|k,k, if (see [])
k–k n|tntn–|<. n=
()
LetA= (anv) be a normal matrix,i.e., a lower triangular matrix of nonzero diagonal entries. ThenAdefines the sequence-to-sequence transformation, mapping the sequence s= (sn) toAs= (An(s)), where
n An(s) =anvsv,n= , , . . . .() v= ©2012 Özarslan and Ari; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • Univers Univers
  • Ebooks Ebooks
  • Livres audio Livres audio
  • Presse Presse
  • Podcasts Podcasts
  • BD BD
  • Documents Documents