Browsing by Author "Savas, Ekrem"

Now showing 1 - 13 of 13

Generalized Hausdorff Matrices as Bounded Operators Over Ak
(Eudoxus Press, Llc, 2009) Savas, Ekrem; Sevli, Hamdullah
In this paper we prove a theorem which shows that a generalized Hausdorff matrix is a bounded operator on A(k), defined below by (2); i.e., (H-beta, mu) is an element of B (A(k))
Lacunary Statistical Convergence of Multiple Sequences
(Pergamon-elsevier Science Ltd, 2006) Savas, Ekrem; Patterson, Richard F.
Quite recently, Mursaleen and Edely [M. Mursaleen, O.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. (in press)], defined the statistical analogue for double sequences x = {(xk,1)} as follows: A real double sequence x = {x(k,l)} is said to be P-statistically convergent to L provided that for each epsilon > 0 P - lim(m,n) 1/mn {numbers of (j, k) : j < m and k < n, vertical bar x(j,k) - L vertical bar >=epsilon}. In this paper we introduce and study lacunary statistical convergence for double sequences and we shall also present some inclusion theorems. (c) 2005 Published by Elsevier Ltd.
Multidimensional Matrix Characterizations of the Banach and Pringsheim Core
(Pergamon-elsevier Science Ltd, 2007) Patterson, Richard F.; Savas, Ekrem
In this paper we shall present a multidimensional invariant Pringsheim core theorem. Conditions on a four-dimensional matrix transformation that will ensure that the transformed Pringsheim core of a bounded double sequence [x] is contained in the double Banach core of [x] shall also be presented. (C) 2006 Published by Elsevier Ltd.
On Absolute Cesaro Summability
(Springer international Publishing Ag, 2009) Sevli, Hamdullah; Savas, Ekrem
Denote by A(k) the sequence space defined by A(k) = {(s(n)) : Sigma(infinity)(n=1) n(k-1)vertical bar a(n)vertical bar(k) < infinity, a(n) = s(n) - s(n-1)} for k >= 1. In a recent paper by E. Savas, and H. Sevli (2007), they proved every Cesaro matrix of order alpha, for alpha > - 1, (C, alpha) is an element of B(A(k)) for k >= 1. In this paper, we consider a further extension of absolute Cesaro summability. Copyright (C) 2009 H. Sevli and E. Savas.
On Almost Convergent Sequences of Fuzzy Numbers
(World Scientific Publ Co Pte Ltd, 2006) Savas, Ekrem
In this paper, we study the space of almost convergent sequences of fuzzy numbers and show that it is complete metric space. We also introduce and discuss the concept of almost statistical convergence of fuzzy numbers.
On Asymptotically (Λ, Σ)-Statistical Equivalent Sequences of Fuzzy Numbers
(Springer, 2010) Savas, Ekrem; Sevli, H.; Cancan, M.
The goal of this paper is to give the asymptotically (lambda, sigma)-statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and lambda-statistical convergence of fuzzy numbers.
On Extension of a Result of Flett for Cesaro Matrices
(Pergamon-elsevier Science Ltd, 2007) Savas, Ekrem; Sevli, Hamdullah
In this work we prove a theorem which shows that a Cesaro matrix of order alpha > -1 is a bounded operator on A(k), defined below by (2); i.e., (C, alpha) is an element of B (A(k)). (C) 2006 Published by Elsevier Ltd.
On Some New Double Sequence Spaces Defined by a Modulus
(Elsevier Science inc, 2007) Savas, Ekrem
In this paper our purpose is to extend some results known in the literature for ordinary (single) sequences to multiply sequences of real and complex numbers. This will be accomplished by presenting the following sequence spaces: {x is an element of s" : P - lim(m,n)Sigma(infinity infinity)(k,l=0,0)a(m,n,k,l)f(vertical bar x(sigma k(p),sigma l(q))vertical bar)(Pk,l) = 0}, {x is an element of s" : P - lim(m,n)Sigma(infinity infinity)(k,l=0,0)a(m,n,k,l)f(vertical bar x(sigma k(p),sigma l(p)) - Le vertical bar)(Pk,l) = 0, for some L}, and {x is an element of s" : sup(m,n,p,q)Sigma(infinity infinity)(k,l=0,0)a(m,n,k,l)f(vertical bar x(sigma(p)sigma l(q))vertical bar)(Pk,l) < infinity} where f is a modulus function, uniformly in (p, q) and A is a nonnegative RH-regular summability matrix method. In addition, we shall give double sigma-statistical convergence. (c) 2006 Elsevier Inc. All rights reserved.
Some Almost Convergent Sequence Spaces of Fuzzy Numbers Generated by Infinite Matrices
(World Scientific Publ Co Pte Ltd, 2006) Savas, Ekrem
In this paper we define some almost convergent sequence spaces of fuzzy numbers by using the A-transforms and we also examine topological properties and some inclusion relations for these new sequence spaces.
Some Σ-Double Sequence Spaces Defined by Orlicz Function
(Academic Press inc Elsevier Science, 2006) Savas, Ekrem; Patterson, Richard F.
In this paper we introduce some new double sequence spaces using the notions of invariant mean and Orlicz function. We also examine some properties of the resulting sequence spaces. (c) 2005 Elsevier Inc. All rights reserved.
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.
Uniformly Summable Double Sequences
(Akademiai Kiado Zrt, 2007) Patterson, Richard F.; Savas, Ekrem
In 1945 Brudno presented the following important theorem: If A and B are regular summability matrix methods such that every bounded sequence summed by A is also summed by B, then it is summed by B to the same value. In 1960 Petersen extended Brudno's theorem by using uniformly summable methods. The goal of this paper is to extend Petersen's theorem to double sequences by using four dimensional matrix transformations and notion of uniformly summable methods for double sequences. In addition to this extension we shall also present an accessible analogue of this theorem.