Some notes on matrix transforms of summability domains of Cesàro matrices

Abstract

In this paper sufficient conditions for a matrix M = (m_nk ) (m_nk are Cesàro numbers A^s _n‐k, s ∈ C if k ≤ n and m_nk= 0 if k > n) to be a transform from the summability domain of the Cesàro method C^α into the summability domain of another Cesàro method C^β , where α, β ∈ C\{-1, -2,…}, are found.

First published online: 09 Jun 2011