Ukr. Mat. Zh. - 2017. - 69, № 12. - pp. 1701-1713
We introduce a one-sided Tauberian condition in terms of the weighted general control modulo oscillatory behavior of integer order $m$ with $m \geq 1$ for the power-series summability method.
Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 928–935
We prove a new Tauberian-like theorem. For a real sequence u = (u n ), on the basis of the weighted mean summability of its generator sequence (V (0) n,p (∆u)) and some other conditions, this theorem establishes the property of slow oscillation of the indicated sequence.