\(C_{\lambda}\)-semiconservative FK-spaces
type: Item
instance of: scholarly article
title: \(C_{\lambda}\)-semiconservative FK-spaces
zbMATH Open document ID: 1269.46005
author: Ilhan Dağadur
published in: Ukrainian Mathematical Journal
publication date: 2013-02-01T00:00:00Z
review text: By the definition given by \textit{A. K. Snyder} and \textit{A. Wilansky} [Rocky Mt. J. Math. 2, No. 4, 595--603 (1972; Zbl 0267.40002)], an FK-space \(X\) containing the unit sequences \(\delta^{k}=\left( \delta_{ki}\right) _{i\in\mathbb{N}}\) \(\left( k\in\mathbb{N}\right) \) is called semiconservative if the series \(\sum_{k}f\left( \delta^{k}\right) \) is convergent for each \(f\in X^{\prime}\). If this series is \(A\)-summable, then we speak of the \(A\)-semiconservativity of \(X\). \textit{H. G. Ince} [Math. Commun. 14, No. 1, 157--165 (2009; Zbl 1184.40006)] considered the case \(A=C\), the Cesàro method. In the paper under review, the author studies \(C_{\lambda}\)-semiconservative FK-spaces, where \(C_{\lambda}\) is the submethod of \(C\) defined by the transformation \(y_{n}=\frac{1}{\lambda_{n}}\sum _{k=1}^{\lambda_{n}}\sum_{i=1}^{k}x_{i}\) \ \(\left( n\in\mathbb{N}\right) \) for an index sequence \(\lambda=\left( \lambda_{n}\right) \).
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 40G05
Mathematics Subject Classification ID: 46A35
zbMATH DE Number: 6133799
zbMATH Keywords: FK-spaces
zbMATH Keywords: semiconservative FK-spaces
zbMATH Keywords: methods of summability
reviewed by: Toivo Leiger
MaRDI profile type: Publication
full work available at URL: s11253-012-0697-y
OpenAlex ID: W1973254919
cites work: A NEW TYPE OF CESÀRO MEAN
cites work: Note on Convergence and Summability Factors
cites work: Convergent and bounded Cesàro sections in \(FK\)-spaces
cites work: Q4795815
cites work: Sequences of bounded variation and sequences of Fourier coefficients. II
cites work: Summen von FK-Räumen. Funktionale Abschnittskonvergenz und Umkehrsätze
cites work: Q3637926
cites work: EQUIVALENCE RESULTS FOR CESÀRO SUBMETHODS
cites work: Q4178057
cites work: Q5509268
cites work: Q3312652
cites work: Inclusion theorems and semiconservative FK spaces
cites work: Q3254442
DOI: 10.1007/S11253-012-0697-Y
description: scientific article; zbMATH DE number 6133799