Browsing by Author "Rhoades, B.E."

Now showing 1 - 7 of 7

Double Summability Factor Theorems and Applications
(Element D.O.O., 2007) Savaş, E.; Rhoades, B.E.
We obtain sufficient conditions for the series ∑ ∑ amn, which is absolutely summable of order k by a double triangular matrix method A, to be such that ∑ ∑ amnλmn is absolutely summable of order k by a double triangular matrix B. As corollaries we obtain a number of inclusion theorems.
General Inclusion Theorems for Absolute Summability of Order K ≥ 1
(Element D.O.O., 2005) Rhoades, B.E.; Savaş, E.
We establish a general inclusion theorem for absolute summability of order k ≥ 1, involving two lower triangular matrices. As corollaries we obtain a number of other inclusion theorems. © ELEMENT, Zagreb.
A Note on Absolute Summability Factors
(2005) Rhoades, B.E.; Savaş, E.
We obtain sufficient conditions for the series sum;. a nλ n to be absolutely summable of order k by a triangular matrix. © Akadémiai Kiadó.
On Inclusion Relations for Absolute Summability
(2002) Rhoades, B.E.; Savaş, E.
We obtain necessary and (different) sufficient conditions for a series summable | N−, pn|k, 1
On Some New Sequence Spaces of Invariant Means Defined by Orlicz Functions
(Element D.O.O., 2002) Savas, E.; Rhoades, B.E.
The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of a Orlicz function, invariant mean and lacunary convergence. We also examine some topological properties of these spaces and establish some elementary connections between lacunary [w]σ -convergence and lacunary [w]σ -convergence with respect to an Orlicz functions which satisfy a Δ2 -condition.
Some Summability Factor Theorems for Absolute Summability
(2002) Rhoades, B.E.; Sava§, E.
We prove a new theorem concerning summability factors. As corollaries we obtain the results of Sulaiman [5]. © 2014, Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München. All rights reserved.
A Summability Factor Theorem for Generalized Absolute Summability
(Michigan State University Press, 2006) Rhoades, B.E.; Savaş, E.
In this paper, we establish a summability factor theorem for summability |A, δ|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.