Browsing by Author "Savas, E."

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Inclusion Theorems for Double Lacunary Sequence Spaces
(Univ Szeged, Bolyai institute, 2005) Savas, E.; Karakaya, Vatan; Patterson, R. F.
In this paper we will present a definition for lacunary P-convergent double sequences analogues to the definition presented by Freedman, Sember and Raphael in 1978. This definition shall be used to establish a connection between the strongly double Cesaro summable and strongly double lacunary convergent sequences, and the connection strongly double almost convergence and strongly double lacunary convergent sequence. Also, we investigate inclusion relations among these spaces.
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 Asymptotically Lacunary Statistical Equivalent Sequences
(Chiang Mai Univ, Fac Science, 2006) Patterson, F.; Savas, E.
This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent, statistically limit and lacunary sequences. Let theta be a lacunary sequence; the two nonnegative sequences [x] and [y] are said to be asymptotically lacunary statistical equivalent of multiple L provided that for every is an element of> 0 lim(r) 1/h(r) broken vertical bar{k is an element of I-r: broken vertical bar X-k/yk - L broken vertical bar >= is an element of} - 0 (denoted by x similar to(sL)(0) y) and simply asymptotically lacunary statistical equivalent if L = 1. In addition, we shall also present asymptotically equivalent analogs of Fridy's and Orhan's theorems in [3].
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.
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.
A Recent Note on Quasi-Power Increasing Sequence for Generalized Absolute Summability
(Springer, 2009) Savas, E.; Sevli, H.
We prove two theorems on vertical bar A,delta vertical bar(k), k >= 1,0 <= delta < 1/k, summability factors for an infinite series by using quasi-power increasing sequences. We obtain sufficient conditions for Sigma a(n)lambda(n) to be summable vertical bar A,delta vertical bar(k), k >= 1, 0 <= delta < 1/k, by using quasi-f-increasing sequences. Copyright (C) 2009 E. Savas, and H. Sevli.
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)).
A Summability Factor Theorem for Absolute Summability Involving Quasi Power Increasing Sequences
(Shiraz Univ, 2006) Savas, E.
We obtain sufficient conditions for the series Sigma a(n)lambda(n) to be absolutely summable of order k by a triangular matrix.
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)}.