Generalized deferred statistical convergence (Q6600448)

In the abstract, the authors describe the genesis of statistical summability theory roughly as follows.\NStatistical convergence has been introduced by Zygmund and has been considered as a summability method by Schoenberg. After the studies of Fast and Steinhaus, the real appearance has started. Since it has many applications in Fourier analysis, Ergodic theory, Number theory, Measure theory, Trigonometric series, Functional analysis, Approximation theory, many authors have investigated this concept from different perspectives and have also extended it. For example, Mursaleen has given the concept of \(\lambda\)-statistical convergence and Savaş has examined the relationship between strong almost convergence and almost \(\lambda\)-statistical convergence. Then Çolak has introduced the concept of statistical convergence of order \(\alpha\) where \(\alpha \in (0,1].\) The relationship between statistical convergence and Cesàro summability is well known and Cesàro summability has been modified by Agnew which is called as deferred Cesàro means. With the motivation of this, Küçükaslan and Yılmaztürk have combined deferred Cesàro mean and statistical convergence.\N\NIn the present paper, the authors introduce the concepts of deferred statistical convergence of order \(\alpha \beta\) and strongly \(s\)-deferred Cesàro summability of order \(\alpha \beta\) for sequences of real or complex numbers. They investigate the properties of these concepts, and the relationships between them are also examined. Furthermore, special cases of these concepts are presented.\N\NFor the entire collection see [Zbl 1521.41001].