Convolution of summability methods

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.

Comparison of Products of Methods of Summability*

determined by the matrix A =(a„fc) of real or complex constants, if the transform S» exists and limn^S„ = L. The matrix A (and method of summability A) is called row-finite if for each n, a„k = 0 for all sufficiently great k; and is called triangular if an* = 0 for k>n. The method A is regular if sn—>L implies Sn-*L. Necessary and sufficient conditions that A be regular are, by the Silverman-To...

Generalization of Some Absolute Summability Methods

Mazhar (1971) gave the characterization for the series ∑ an n to be summable |N,pn|whenever ∑ an is summable |C,α|k, α≥ 0, k≥ 1. Here we prove two theorems, the first concerns the sufficient conditions and the second the necessary conditions satisfied by { n } in order to have ∑ an n summable |N̄,pn|k whenever ∑ an is summable |C,α|k, k≥ 1. 2000 Mathematics Subject Classification. Primary 40G. L...