On $\vert \overline N,p\sb n\vert \sb k$ summability factors

q|k Summability Factors of Infinite Series

W. T. Sulaiman Department of Computer Engineering, College of Engineering, University of Mosul, Mosul, Iraq Correspondence should be addressed to W. T. Sulaiman, [email protected] Received 5 November 2010; Accepted 19 January 2011 Academic Editor: Paolo E. Ricci Copyright q 2011 W. T. Sulaiman. This is an open access article distributed under the Creative Commons Attribution License, whi...

A note on | A | k summability factors of infinite series

A weighted mean matrix, denoted by (N , pn), is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn := ∑n k=0 pk. Mishra and Srivastava [1] obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix (N , pn). Bor [2] extended this result to absolute sum...

On absolute Nörlund summability factors

A note on absolute summability factors

A note on absolute summability factors

A sequence (bn) of positive numbers is said to be δ -quasi-monotone, if bn → 0, bn > 0 ultimately and ∆bn ≥ −δn, where (δn) is a sequence of positive numbers (see [3]). Let (φn) be a sequence of complex numbers and let ∑an be a given infinite series with partial sums (sn). We denote by σα n and tα n the nth Cesàro means of order α , with α > −1, of the sequences (sn) and (nan), respectively, i.e.,