A study on absolute summability factors for a triangular matrix

A note on absolute summability factors

On absolute matrix summability methods

On Absolute Matrix Summability Methods

We have proved a theorem on |T, p n | k summability methods. This theorem includes a known theorem.

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.,

Absolute matrix summability methods