Summability factors between the absolute Cesàro methods

Factors for generalized absolute Cesàro summability

A positive sequence (bn) is said to be almost increasing if there exists a positive increasing sequence cn and two positive constants A and B such that Acn ≤ bn ≤ Bcn (see [1]). Obviously every increasing sequence is almost increasing but the converse need not be true as can be seen from the example bn = ne(−1) n . Let ∑ an be a given infinite series with partial sums (sn). We denote by tn n-th...

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.

Absolute matrix summability methods

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.