Tauberian theorems for the statistical convergence and the statistical (C,1,1) summability
Makaleler > Tam Makale · 2018
Yazarlar: Umit Totur, İbrahim ÇANAK
Filomat, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2018, cilt 32, ss 101-116
DOI: 10.2298/fil1801101t
Özet
Every P-convergent double sequence is statistically convergent and every bounded statistically convergent sequence is statistical (C,1,1) summable. The converse of these implications are not always true. Theorems on which conditioned converses are searched are known as Tauberian theorems. Inspired by the convergence to zero of the difference sequence between a sequence and its arithmetic means in the single sequence case, we obtain Tauberian theorems for the statistical convergence and statistical (C,1,1) summability method by imposing some conditions on the difference sequence between a double sequence and its different arithmetic means.