Criteria for statistical convergence with respect to power series methods
type: Item
instance of: scholarly article
title: Criteria for statistical convergence with respect to power series methods
zbMATH Open document ID: 1473.40005
author: Nilay Şahin Bayram
published in: Positivity
publication date: 2021-08-16T00:00:00Z
review text: The concept of statistical convergence with respect to power series methods was introduced by \textit{M. Ünver} and \textit{C. Orhan} [Numer. Funct. Anal. Optim. 40, No. 5, 535--547 (2019; Zbl 1430.40004)]. Using this newly defined concept, the following results are obtained by the author. A decomposition theorem is given and an analogue of a criterion by \textit{I. J. Schoenberg} [Am. Math. Mon. 66, 361--375, 562--563 (1959; Zbl 0089.04002)] is derived for \(P\)-statistical convergence. A result by \textit{T. Šalát} [Math. Slovaca 30, 139--150 (1980; Zbl 0437.40003)] is extended to \(P\)-statistical convergence. Moreover, the question ``How much room is there between \(st_P\) and \(w(P)\)?'', where \(w(P)\) and \(st_P\) respectively denote the sets of all \(P\)-strongly convergent and \(P\)-statistically convergent sequences, is answered. We note that a similar question was answered by \textit{J. Connor} et al. [Analysis, München 22, No. 4, 321--333 (2002; Zbl 1030.40004)] for \(A\)-statistical convergence and \(A\)-strong convergence, where \(A\) is a nonnegative regular matrix.
reviewed by: İbrahím Çanak
Mathematics Subject Classification ID: 40G15
Mathematics Subject Classification ID: 40C15
Mathematics Subject Classification ID: 40F05
zbMATH DE Number: 7382087
zbMATH Keywords: power series method
zbMATH Keywords: statistical convergence
zbMATH Keywords: strong convergence
zbMATH Keywords: uniform integrability
zbMATH Keywords: inverse Fourier transformation
zbMATH Keywords: factorizing of sequences
MaRDI profile type: Publication
full work available at URL: s11117-020-00801-6
OpenAlex ID: W3121046661
cites work: Q4520851
cites work: ON STATISTICAL CONVERGENCE
cites work: MULTIPLIERS AND FACTORIZATIONS FOR BOUNDED STATISTICALLY CONVERGENT SEQUENCES
cites work: Sequential definitions of continuity for real functions.
cites work: A criterion for \(A\)-statistical convergence
cites work: Tauberian theorems for \(J_ p\)-summability
cites work: On statistically convergent and statistically Cauchy sequences
cites work: Q3878090
cites work: The Integrability of Certain Functions and Related Summability Methods
cites work: On certain families of generalized Nörlund methods and power series methods
cites work: Statistical Convergence with Respect to Power Series Methods and Applications to Approximation Theory
DOI: 10.1007/S11117-020-00801-6
description: scientific article; zbMATH DE number 7382087