Tauberian Conditions with Controlled Oscillatory Behavior for Statistical Convergence

Abstract

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 ->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.