A new note on generalized absolute matrix summability

A note on generalized absolute Cesàro summability

In this paper, a known theorem dealing with | C, 1 |k summability methods has been generalized under weaker conditions for | C, α, β ; δ |k summability methods. Some new results have also been obtained. AMS subject classifications: 40D15, 40F05, 40G99

A note on absolute summability factors

On generalized absolute Cesàro summability

In this paper, a main theorem dealing with | C, 1 |k summability factors has been generalized under more weaker conditions for | C,α, β |k summability factors. This theorem also includes some new results. Mathematics Subject Classification 2000: 40D15, 40F05, 40G05, 40G99.

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.,

On absolute matrix summability methods