Results 21 to 30 of about 50 (49)

Matrix transformations of starshaped sequences

International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 4, Page 189-200, 2001., 2001
We deal with matrix transformations preserving the starshape of sequences. The main result gives the necessary and sufficient conditions for a lower triangular matrix A to preserve the starshape of sequences. Also, we discuss the nature of the mappings of starshaped sequences by some classical matrices.
Chikkanna R. Selvaraj, Suguna Selvaraj
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

Double sequence core theorems

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
wiley   +1 more source

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
wiley   +1 more source

A Novel Conservative Matrix Arising From Schröder Numbers and Its Properties

Linear and Multilinear Algebra, 2023
Muhammet Cihat Dagli
exaly