Browsing by Author "Rhoades, B. E."

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A Note on |a|k Summability Factors
(Pergamon-elsevier Science Ltd, 2007) Savas, E.; Rhoades, B. E.
We obtain sufficient conditions for the series Sigma a(n)lambda(n) to be absolutely summable of order k by a triangular matrix. (c) 2006 Elsevier Ltd. All rights reserved.
On the Cesaro Summability of Double Series
(Springer international Publishing Ag, 2008) Savas, E.; Sevli, H.; Rhoades, B. E.
In a recent paper by Savas, and Sevli (2007), it was shown that each Cesaro matrix of order alpha, for alpha > -1, is absolutely kth power conservative for k >= 1. In this paper we extend this result to double Cesaro matrices. Copyright (C) 2008.
On |a|k Summability Factors
(Springer, 2006) Rhoades, B. E.; Savas, E.
The paper deals with absolute summability factors for infinite series. The main result obtained in this paper generalizes a recent paper of Mazhar.
Sufficient Conditions for Factorable Matrices To Be Bounded Operators on Ak
(Rocky Mt Math Consortium, 2009) Savas, E.; Sevli, H.; Rhoades, B. E.
A factorable matrix A is a lower triangular matrix with entries a(nk) = a(n)b(k). The sequence space A(k) is defined in (2). In this paper we determine sufficient conditions for a nonnegative factorable matrix A to be a bounded operator on A(k), i.e., A is an element of B(A(k)). As corollaries we obtain sufficient conditions for the discrete Cesdro, terraced, and P-Cesaro matrices defined by Rhaly, to be in B(A(k)).
Summability Factor Theorem for Generalized Absolute Summability
(Michigan State Univ Press, 2005) Rhoades, B. E.; Savas, Ekrem
In this paper, we establish a summability factor theorem for summability vertical bar A, delta vertical bar(k) as defined in (1) where A is a lower triangular matrix with non-negative entries satisfying certain conditions. Our paper is an extension of the main result of [1] using definition (1) below.
Summability Factor Theorems for Triangular Matrices
(Eudoxus Press, Llc, 2007) Savas, Ekrem; Rhoades, B. E.
We obtain necessary and sufficient conditions for the series Sigma a(n) summable \A\ to imply that Sigma a(n)lambda(n) is summable \B\(k), and for the series Sigma(an) summable \A\(k) to imply that Sigma a(n)lambda(n) is summable \B\, k >= 1 where A and B are lower triangular matrices.
Triangles Which Are Bounded Operators on Ak
(Malaysian Mathematical Sciences Soc, 2009) Savas, E.; Sevli, H.; Rhoades, B. E.
A lower triangular infinite matrix is called a triangle if there are no zeros on the principal diagonal. The main result of this paper gives a minimal set of sufficient conditions for a triangle T : A(k) -> A(k) for the sequence space A(k) defined as follows: A(k) := {{s(n)} : (n=1)Sigma(infinity)n(k-1)vertical bar a(n)vertical bar(k) < infinity, a(n) = s(n) - s(n-1)}.