Criteria for statistical convergence with respect to power series methods
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.
scientific article; zbMATH DE number 7382087