Inclusion results on statistical cluster points (Q1677536)

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.].