Abstract
In this paper, a general theorem dealing with the φ − ∣ A ; δ ∣ k summability method has been proved. This theorem also includes some known results.
Highlights
IntroductionA defines the sequence-to-sequence transformation, mapping the sequence s = (sn) to As = (An(s)), where n
Let an be a given infinite series with the partial sums, and let A = be a normal matrix, i.e., a lower triangular matrix of non-zero diagonal entries
Bor [2] has proved the following theorem for | N, pn |k summability of infinite series
Summary
A defines the sequence-to-sequence transformation, mapping the sequence s = (sn) to As = (An(s)), where n. Defines the sequence (tn) of the (N , pn) mean of the sequence (sn), generated by the sequence of coefficients (pn) (see [3]). The series an is said to be summable | N , pn |k, k ≥ 1, if (see [1]). In the special case when pn = 1 for all n, | A, pn |k summability is the same as. Bor [2] has proved the following theorem for | N , pn |k summability of infinite series. Vav , v=1 anλn is summable | N , pn |k, k ≥ 1
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