Some gap Tauberian remainder theorems are proved for generalized linear methods A = (Ank) , where Ankare bounded linear operators from Banach space X into X. In these theorems the investigated sequences have infinitely many constant pieces.
Meronen, O., & Tammeraid, I. (2008). Generalized linear methods and gap tauberian remainder theorems. Mathematical Modelling and Analysis, 13(2), 223-232. https://doi.org/10.3846/1392-6292.2008.13.223-232
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