Abstract
In this paper, a known theorem dealing with weighted mean summability methods of non-decreasing sequences has been generalized for |A,p_{n};δ|_{k} summability factors of almost increasing sequences. Also, some new results have been obtained concerning |N,p_{n}|_{k}, |N,p_{n};δ|_{k} and |C,1;δ|_{k} summability factors.
Highlights
P Let an be a given in...nite series with the partial sums
Bor has proved the following theorems concerning on weighted arithmetic mean summability factors of in...nite series
If we take = 0 in Theorem 9, Theorem 9 reduces to jA; pnjk summability theorem
Summary
P Let an be a given in...nite series with the partial sums (sn). We denote un the nth Cesaro mean of order , with > 1, of the sequence (sn), that is (see [9]),. If we take = 0, we have jC; jk summability (see [12]). Let (pn) be a sequence of positive numbers such that. The series an is said to be summable jN ; pn; jk, k 1 and. Let A = (anv) be a normal matrix. Given a normal matrix A = (anv), we associate two lower semimatrices A = (anv) and A^ = (a^nv) as follows: Xn anv = ani; n; v = 0; 1; :::. =1 for all n, jA; pn; jk summability is the same as jC; 1jk summability
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