Tauberian conditions with controlled oscillatory behavior for statistical convergence
Articles > Article · 2018
Authors: Sefa Anıl Sezer, Rahmet Savaş, İbrahim ÇANAK
Filomat, Journal Indexed in SCI Expanded, International, Scopus, 2018, vol 32, pp 3853-3865
DOI: 10.2298/FIL1811853S
Summary
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 (Formula presented), where ξ 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.