Inclusion relations among methods of summability compounded from given matrix methods

Absolute matrix summability methods

Inclusion Theorems for Absolute Summability Methods

In this paper we have proved two theorems concerning an inclusion between two absolute summability methods by using any absolute summability factor.

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 Inclusion Relations for Absolute Summability

We obtain necessary and (different) sufficient conditions for a series summable | ¯ N, p n | k , 1 < k ≤ s < ∞, to imply that the series is summable |T | s , where (¯ N, p n) is a weighted mean matrix and T is a lower triangular matrix. As corollaries of this result, we obtain several inclusion theorems. Let a n be a given series with partial sums s n , (C, α) the Césaro matrix of order α. If σ...