@article{Mulyava_Sheremeta_2013, title={Remarks on sufficient conditions of belonging of analytic functions to convergence classes}, volume={5}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/1320}, DOI={10.15330/cmp.5.2.298-304}, abstractNote={It is well known that if Taylorâ€™s coefficientsÂ $f_n$ of an entire functions $f$ satisfy the conditions $|f_k|/|f_{k+1}|
earrow +\infty$ as $k\to\infty$ and $\sum\limits_{k=1}^{\infty}|f_k|^{\varrho/k}<+\infty$ then $f$ belongs to Valiron convergence class. It is proved that in the statement the condition $|f_k|/|f_{k+1}|
earrow +\infty$ one can replace on the condition $l_{k-1}l_{k+1}l^{-2}_{k}|f_k|/|f_{k+1}|
earrow +\infty$, where $(l_k)$ is a positive sequence such that $\root{k}\of{l_k/l_{k+1 }\asymp 1$ as $k\to\infty$. Analogous problems are solved for another convergence classes of entire and analytic functions in the unit disk.}, number={2}, journal={Carpathian Mathematical Publications}, author={MulyavaO.M. and SheremetaM.M.}, year={2013}, month={Dec.}, pages={298-304} }