Matrix summability in $F$-fields

Matrix Summability in 7"-fields

when un = 22"-o a-inUi for all ra^O. If the sequence to sequence transformation associated with A is such that [u/[ ] exists and converges whenever [un] converges we call A a K matrix. If [uJ ] exists and converges to limn,,, un whenever this limit exists we call A a T matrix. Similar names for the series to sequence and the series to series matrices are TCi, 7\ and K2, T2 matrices respectively...

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.

On absolute matrix summability of orthogonal series

In this paper, we prove two theorems on ∣A∣k, 1 ≤ k ≤ 2, summability of orthogonal series. The first one gives a sufficient condition under which an orthogonal series is absolutely summable almost everywhere, and the second one, is a general theorem, which also gives a sufficient condition so that an orthogonal series is absolutely summable almost everywhere, but it involves a positive numerica...