Statistical Deferred Cesàro Summability and Its Applications to Tauberian Theory
Makaleler > Tam Makale · 2023
Yazarlar: Sefa Anil Sezer, Zerrin Onder, İbrahim ÇANAK
Bulletin of the Iranian Mathematical Society, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2023, cilt 49
DOI: 10.1007/s41980-023-00770-y
Özet
Our aim in this paper is to make a novel interpretation of the relation between the statistical deferred Cesaro summability method and statistical convergence based on a certain subsequence for sequences of real or complex numbers. In line with this aim, we introduce a necessary and sufficient Tauberian condition of Moricz-type for statistically deferred Cesaro summable sequences. In addition, we define the concepts of statistical deferred slow decrease and statistical deferred slow oscillation for a sequence of real and complex numbers, respectively. As a result, we derive some Tauberian conditions controlling O-L- and O-oscillatory behavior of a sequence in the statistical sense.