Browsing by Author "Savaş, E."

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Almost Regular Matrices for Double Sequences
(2003) Mursaleen,; Savaş, E.
In this paper we define and characterize the almost regular matrices for double sequences and further we apply these matrices to establish a core theorem. © 2003 Akadémiai Kiadó, Budapest.
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 Relations for Absolute Summability
(Element D.O.O., 2005) Savaş, E.
We obtain sufficient conditions for the series ∑an, which is absolutely summable of order k by a triangular matrix method A, 1 < k ≤ s < ∞, to be such that ∑an is absolutely summable of order s by a triangular matrix B. As corollaries, we obtain a number of inclusion theorems. © ELEMENT, Zagreb.
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.
A Note on Double Sequences of Fuzzy Numbers
(1996) Savaş, E.
In this paper we introduce double convergent sequences of fuzzy numbers and we also study the space of double convergent sequences of fuzzy numbers. © TÜBİTAK.
On Almost Increasing Sequences for Generalized Absolute Summability
(Element D.O.O., 2006) Savaş, E.
In this paper, we establish a summability factor theorem for summability |A, δ|k as defined in (2) where A is a lower triangular matrix with non-negative entries satisfying certain conditions. This paper is an extension of the main result of [3] using definition (2) below. Let A be a lower triangular matrix, {sn} a sequence. Then An := ∑v=0nanvsv. A series ∑a n is said to be summable |A|k, k ≥ 1 if ∑n=1∞ nk-1|An - A n-1|k < ∞. (1) and it is said to be summable |A, δ|k, k ≥ 1 and δ ≥ 0 if (see,[1]) ∑n=1∞ nδk+k-1|An - An-1|k < ∞. © ELEMENT.
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 Sequence Spaces and S-Convergence
(Walter de Gruyter GmbH, 2000) Savaş, E.
The purpose of this paper is to introduce some sequence spaces and also give some inclusion relations between sequence spaces and s-convergence. © 2000 Warsaw University. All rights reserved.
On Some Sequence Spaces and Lacunary Σ-Statistical Convergence
(Association for Scientific Research, 2003) Savaş, E.; Savaş, R.
In this note , we define and study two concepts which arise from the notion of lacunary strong convergence, and invariant means, namely lacunary strong $sigma$- convergence with respect to an Orlicz function and lacunary a-statistical convergence and established the relationship between these two concepts.
On |a, Δ|k Summability Factors
(EUT Edizioni Universita di Trieste, 2006) Savaş, E.
We obtain sufficient conditions for the series Σ anλn to be absolutely summable of order k by a triangular matrix. © 2003, EUT Edizioni Universita di Trieste.
An Orlicz Extension of Some New Sequence Spaces
(EUT Edizioni Universita di Trieste, 2005) Savaş, E.; Patterson, R.F.
The aim of this note is to introduce and study a new concept of lacunary σ-convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. © 2005 EUT Edizioni Universita di Trieste.
Some Sequence Spaces Defined by Orlicz Functions
(2004) Savaş, E.; Savaş, R.
In this paper we introduce a new concept of λ-strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. It is also shown that if a sequence is λ-strongly convergent with respect to an Orlicz function then it is λ-statistically convergent.
Strong Almost Convergence and Almost Λ-Statistical Convergence
(2000) Savaş, E.
The purpose of this paper is to define almost λ-statistical convergence by using the notion of (V, λ)-summability to generalize the concept of statistical convergence. © 2000 by the University of Notre Dame. 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.
A Summability Factor Theorem for Infinite Series
(Michigan State University Press, 2004) Savaş, E.
We obtain sufficient conditions for the series Σ anλn to be absolutely summable of order k by a triangular matrix.
Σ-Asymptotically Lacunary Statistical Equivalent Sequences
(2006) Savaş, E.; Patterson, R.F.
This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let θ be a lacunary sequence; Two nonnegative sequences [χ] and [y] are Sσ,θ-asymptotically equivalent of multiple L provided that for every ε > 0 limr 1/hr {k ε Ir: xσκ(m)/yσk(m) - L ≥ ε} = 0 uniformly in m = 1, 2, 3,..., (denoted by x ∼ Sσ,θy) simply Sσ,θ -asymptotically equivalent, if L = 1. Using this definition we shall prove Sσ,θ-asymptotically equivalent analogues of Fridy and Orhan's theorems in [5] and analogues results of Das and Patel in [1] shall also be presented. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2006.