Tauberian conditions with controlled oscillatory behavior for statistical convergence

Sefa Anıl Sezer, Rahmet Savaş, İbrahim Çanak


We present new Tauberian conditions in terms of the general logarithmic control modulo of the oscillatory behavior of a real sequence $(s_n)$ to obtain
$$\lim_{n\to\infty}s_n=\xi \ \ \text{from} \ st-\lim_{n\to\infty}s_n=\xi,$$
where $\xi$ is a finite number. We also introduce the statistical $(\ell,m)$ summability method and extend some Tauberian theorems to this method. The main results improve some well-known Tauberian theorems obtained for the statistical convergence.


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