Abstract
In the present paper, we have proved theorems dealing with matrix summability factors by using quasi β-power increasing sequences. Some new results have also been obtained.MSC:40D15, 40F05, 40G99.
Highlights
A positive sequence is said to be quasi β-power increasing sequence if there exists a constant K = K(β, γ ) ≥ such that Knβ γn ≥ mβ γm holds for all n ≥ m ≥ [ ]
If we take pn = in these theorems, we have two new results dealing with |A|k summability factors of infinite series
By taking (Xn) as almost increasing sequence in the theorems, we get new results dealing with |A, pn|k summability factors of infinite series
Summary
A positive sequence (γn) is said to be quasi β-power increasing sequence if there exists a constant K = K(β, γ ) ≥ such that Knβ γn ≥ mβ γm holds for all n ≥ m ≥ [ ]. Let an be a given infinite series with the partial sums (sn). Let (pn) be a sequence of positive numbers such that n. Let A = (anv) be a normal matrix, i.e., a lower triangular matrix of nonzero diagonal entries. A defines the sequence-to-sequence transformation, mapping the sequence s = (sn) to As = (An(s)), where n. Given a normal matrix A = (anv), we associate two lower semimatrices A = (anv) and. Theorem A Let (Xn) be a quasi β-power increasing sequence for some < β < , and let there be sequences (βn) and (λn) such that.
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