In this paper, a general theorem on N, p ; ␦ summability factors of infinite k n series has been proved under suitable conditions by using an almost increasing sequence.
On translativity of absolute Riesz summability
✍ Scribed by Mehmet Ali Sarıgöl
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 218 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
In this work we characterize translativity of the summability |R, p n | k , k > 1, for any sequence (p n ) without imposing the conditions given by Orhan [C. Orhan, Translativity of absolute weighted mean summability, Czechoslovak Math. J. 48 (1998) 755-761], and so deduce some known results.
📜 SIMILAR VOLUMES
of Denton (Texas) (Eingegangen am 4.6. 1971) ## 1. Definitions Let a, be a giveninfinite series and let A, = il (n) be a positive inonotonic function of n tending t o infinity with n. We write The series z c n , i s said to he summable (R, An, r ) , r 2 0, t o sum s, if A > ( w ) / w ' --+ s, as
In this paper, a general theorem on |A, δ| k -summability factors which generalize a theorem of Savas ¸[E. Savas ¸, On a recent result on absolute summability factors, Appl. Math. Lett. 18 (2005) 1273-1280] on |A| k -summability factors has been proved.