Results 21 to 30 of about 65 (64)
Noninclusion theorems: some remarks on a paper by J. A. Fridy
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 2, Page 119-122, 2000., 2000 In 1997, J. A. Fridy gave conditions for noninclusion of ordinary and of absolute summability domains. In the present note, these conditions are interpreted in a natural topological context thus giving new proofs and also explaining why one of these conditions is too weak. Also an open question posed in Fridy′s paper is answered.
W. Beekmann
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Lacunary statistical convergence and inclusion properties between lacunary methods
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 3, Page 175-180, 2000., 2000 A lacunary sequence is an increasing integer sequence θ = {kr} such that kr − kr−1 → ∞ as r → ∞. A sequence x is called sθ‐convergent to L provided that for each ϵ > 0, limr(1/(kr − kr−1)){the number of kr−1 < k ≤ kr : |xk − L| ≥ ϵ} = 0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.
Jinlu Li
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On some topological properties of generalized difference sequence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 11, Page 785-791, 2000., 2000 We obtain some topological results of the sequence spaces Δm(X), where Δm(X) = {x = (xk) : (Δmxk) ∈ X}, (m ∈ ℕ), and X is any sequence space. We compute the pα‐, pβ‐, and pγ‐duals of l∞, c, and c0 and we investigate the N‐(or null) dual of the sequence spaces Δm(l∞), Δm(c), and Δm(c0).
Mikail Et
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The ℓ‐translativity of Abel‐type matrix
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 3, Page 189-195, 2000., 2000 Lemma introduced the Abel‐type matrix Aα,t defined by ank=(k+α k)tnk+1(1−tn)α+1, where α > −1, 0 < tn < 1, for all n, and limtn = 1; and studied it as mappings into ℓ. In this paper, we extend our study of this matrix and investigate its translativity in the ℓ‐ℓ setting.
Mulatu Lemma
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Abel‐type weighted means transformations into ℓ
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 3, Page 197-204, 2000., 2000 Let qk=(k+α k) for α > −1 and Qn=∑k=0nqk. Suppose Aq = {ank}, where ank = qk/Qn for 0 ≤ k ≤ n and 0 otherwise. Aq is called the Abel‐type weighted mean matrix. The purpose of this paper is to study these transformations as mappings into ℓ. A necessary and sufficient condition for Aq to be ℓ‐ℓ is proved.
Mulatu Lemma, George Tessema
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Some saturation classes for deferred Riesz and deferred Nörlund means [PDF]
One of main problem in approximation theory is determining a saturation class for a given method. The problem of determining a saturation class has been considered by Zamanski, Sunouchi, Watari and others. Mohaparta and Russel have considered some direct
ÇATAL, Cumali +2 more
core +2 more sources
q-Stirling sequence spaces associated with q-Bell numbers
Open MathematicsIn this study, we build qq-analog of the qq-Stirling matrix involved qq-Bell numbers Sq=(Snk(q)){{\mathbb{S}}}_{q}=({S}_{nk}\left(q)) defined by Sq=(Snk(q))=Sq(n,k)Bq(n),0≤k≤n,0,otherwise.\begin{array}{r}{{\mathbb{S}}}_{q}=({S}_{nk}\left(q))=\left ...
Atabey Koray Ibrahim +3 more
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The Abel‐type transformations into ℓ
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 4, Page 775-784, 1999., 1999 Let t be a sequence in (0, 1) that converges to 1, and define the Abel‐type matrix Aα,t by for α > −1. The matrix Aα,t determines a sequence‐to‐sequence variant of the Abel‐type power series method of summability introduced by Borwein in [1]. The purpose of this paper is to study these matrices as mappings into ℓ.
Mulatu Lemma
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International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 4, Page 785-793, 1999., 1999 In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined.
Richard F. Patterson
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Noninclusion theorems for summability matrices
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 511-516, 1997., 1997 For both ordinary convergence and ℓ1‐summability explicit sufficient conditions on a matrix have long been known that ensure that the summability method is strictly stronger than the identity map. The main results herein show that a matrix that satisfies those conditions can be included by another matrix only if the other matrix satisfies those same ...
J. A. Fridy
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