The effects of matrix summability methods on bounds of function sequences.
type: Item
instance of: scholarly article
title: The effects of matrix summability methods on bounds of function sequences.
zbMATH Open document ID: 1057.40003
author: Xianqiang Yang
published in: Applied Mathematics Letters
publication date: 2005-03-07T00:00:00Z
review text: Let \(A\) be an infinite matrix, \(\mathcal{F}\) a space of function sequences, \(A\mathcal{F} := \sum_{k = 1}^{\infty}a_{nk}f_k(x)\). The symbol \(G(\mathcal{F}; D)\) denotes the least upper bound of the element \(f_n(x)\) over the subset \(D\). \textit{R. P. Agnew} [Trans. Am. Math. Soc. 32, 669--708 (1930; JFM 56.0213.01)] obtained necessary and sufficient conditions on \(A\) for \(\lim \inf G(\mathcal{F}; D) \leq \lim \inf G(A\mathcal{F}; D) \leq \lim \sup G(A\mathcal{F}; D) \leq \lim \sup G(\mathcal{F}; D)\). In this paper the author obtains the corresponding results with the outsides of this inequality replaced by \(\lim \inf\) and \(\lim \sup\) of the statistical limit of a regular matrix transformation \(T\) of \(G(\mathcal{F}; D)\), respectively.
Mathematics Subject Classification ID: 40C05
zbMATH DE Number: 2140808
zbMATH Keywords: \(T\)-density
zbMATH Keywords: \(T\)-statistical convergence
zbMATH Keywords: \(T\)-statistical cluster point
zbMATH Keywords: \(T\)-statistical limit superior and inferior
zbMATH Keywords: uniformly bounded function sequence
reviewed by: Billy E. Rhoades
MaRDI profile type: Publication
full work available at URL: j.aml.2004.04.003
OpenAlex ID: W2013940708
cites work: Q5788558
cites work: Densities and summability
cites work: A MATRIX CHARACTERIZATION OF STATISTICAL CONVERGENCE
cites work: Matrix Summability of Statistically Convergent Sequences
cites work: A Measure Theoretical Subsequence Characterization of Statistical Convergence
cites work: Sur la convergence statistique
cites work: ON STATISTICAL CONVERGENCE
cites work: Statistical Limit Points
cites work: On almost convergent and statistically convergent subsequences
cites work: On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence
cites work: Generalized statistical convergence and convergence free spaces
cites work: Statistical limit superior and limit inferior
cites work: On statistical limit points and the consistency of statistical convergence
cites work: A-STATISTICAL CORE OF A SEQUENCE
cites work: Statistical core theorems
cites work: Q4779577
cites work: An extension of Knopp's core theorem
DOI: 10.1016/J.AML.2004.04.003
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description: scientific article; zbMATH DE number 2140808