Inclusion results on statistical cluster points
type: Item
instance of: scholarly article
title: Inclusion results on statistical cluster points
zbMATH Open document ID: 1389.40017
published in: Analysis Mathematica
publication date: 2017-11-10T00:00:00Z
review text: The authors study, starting from a nonnegative regular matrix \(A\), the concepts of statistical cluster point, statistical core of a sequence (studied for a Cesàro matrix by \textit{K. Demirci} [Glas. Mat., III. Ser. 37, No. 2, 293--301 (2002; Zbl 1023.40001)]) and the connection between \(A_\lambda\)-statistical convergence and \(A_\mu\)-statistical convergence (\(A_\lambda\), \(A_\mu\) arising from \(A\) above by deleting some rows), studied before by \textit{G. M. Petersen} [J. Lond. Math. Soc. 31, 324--326 (1956; Zbl 0072.05502)]. The layout of the paper is as follows: \textbf{\S1 Introduction} The concepts mentioned are introduced and previous results are discussed. \textbf{\S2 \(A_\lambda\)-statistical cluster points} The main result (Theorem 1) states a relation between \(\delta_{A_\lambda}\) and \(\delta_{A_\mu}\). Moreover, other results are proved; all under weaker conditions than in [K. Demirci, loc. cit.]. \textbf{\S3 \(A\)-statistical inclusion} Definition of the concept; the main result (Theorem 4) is a statistical version of Theorem 1 from [G. M. Petersen, loc. cit.].
reviewed by: Marcel G. de Bruin
Mathematics Subject Classification ID: 40A35
Mathematics Subject Classification ID: 26A03
Mathematics Subject Classification ID: 11B05
zbMATH DE Number: 6806085
zbMATH Keywords: \(A\)-density
zbMATH Keywords: \(A\)-statistical cluster point
zbMATH Keywords: \(A\)-statical core of a sequence
author: Harry I. Miller
author: Leila Miller-Van Wieren
author: Emre Taş
author: T. Yurdakadim
MaRDI profile type: Publication
full work available at URL: s10476-016-0205-y
OpenAlex ID: W2472281837
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DOI: 10.1007/S10476-016-0205-Y
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description: scientific article; zbMATH DE number 6806085