Tauberian theorems for Cesàro summability of nth sequences

Abstract

Tauberian theorem provides a criterion for the convergence of non convergent (summable) sequences. In this paper, we established a Tauberian theorem for nth real sequences via Cesaro summability by
using de la Vallee Poussin mean and slow oscillation. The discussion and ndings are capable to unify several useful concepts in the literature, and also capable to provide nontrivial extension of several useful results. Some examples are also discussed in support of our denitions and results. The findings are further expected to be helpful in designing and study several other interesting problems in summability theory and applications.