Sezer, Sefa AnilSavas, RahmetCanak, Ibrahim2019-10-272019-10-2720180354-51800354-5180https://doi.org/10.2298/FIL1811853Shttps://hdl.handle.net/11454/30854We 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 ->infinity) s(n) = xi from st - lim(n ->infinity) s(n = xi,) where xi is a finite number. We also introduce the statistical (l, 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.en10.2298/FIL1811853Sinfo:eu-repo/semantics/closedAccessTauberian theoremsstatistical convergencelogarithmic summability methodone-sided Tauberian conditionsslowly decreasing sequenceArticle321138533865WOS:000461181900009N/AQ2