Browsing by Author "Rhoades, BE"

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A Characterization of Absolute Summability Factors
(Mathematical Soc Rep China, 2004) Rhoades, BE; Savas, E
Let A and B be two summability methods. We shall use the notation lambda is an element of (A, B) to denote the set of all sequences lambda such that Sigmaa(n)lambda(n) is summable B, whenever Sigmaa(n) is summable A. In the present paper we characterize the sets lambda is an element of (\N,p(n)\, \T\(k)) and lambda is an element of (\(N) over bar ,p(n)\, \T\), where T is a lower triangular matrix with positive entries and row sums 1. As special cases we obtain summability factor theorems and inclusion theorems for pairs of weighted mean matrices.
Some Necessary Conditions for Absolute Matrix Summability Factors
(indian Nat Sci Acad, 2002) Rhoades, BE; Savas, E
We obtain necessary conditions for a lower triangular matrix to have the property that Sigma a(n) lambda(n) is summable \ T \(k) whenever the series Sigma a(n) is bounded \ T \(k).
A Summability Factor Theorem and Applications
(Elsevier Science inc, 2004) Rhoades, BE; Savas, E
We obtain sufficient conditions for the series Sigma a(n), which is absolutely summable of order k by a weighted mean method, to be such that Sigma epsilon(n)a(n) is absolutely summable of order k by a triangular matrix. As corollaries we obtain a number of inclusion theorems. (C) 2003 Elsevier Inc. All rights reserved.
Local Property of Absolute Weighted Mean Summability of Fourier Series
(Elsevier Science inc, 2004) Rhoades, BE; Savas, E
We obtain a theorem on a local property of \N, p(n)\(k), summability of factored Fourier series and a summability factor theorem for Fourier series. (C) 2003 Elsevier Inc. All rights reserved.
Necessary and Sufficient Conditions for Inclusion Relations for Absolute Summability
(indian Academy Sciences, 2003) Rhoades, BE; Savas, E
We obtain a set of necessary and sufficient conditions for \N.p(n)\(k) to imply \(N) over bar ,q(n)\(s) for 1 < k less than or equal to s < infinity. Using this result we establish several inclusion theorems as well as conditions for the equivalence of \(N) over bar ,p(n)\(k) and \(N) over bar ,q(n)\(s).