General logarithmic control modulo and Tauberian remainder theorems

Year 2024, Volume: 73 Issue: 2, 391 - 398, 21.06.2024

Muhammet Ali Okur

https://doi.org/10.31801/cfsuasmas.1380675

Abstract

Let $\lambda=(\lambda_n)$ be a nondecreasing sequence of positive numbers such that $\lambda_n\to\infty$. A sequence $(\xi_n)$ is called $\lambda$-bounded if \begin{equation*} \lambda_n(\xi_n-\alpha)=O(1)\end{equation*} with the limit $\displaystyle{\lim_{n\rightarrow \infty}\xi_n=\alpha}$. In this work, we obtain several Tauberian remainder theorems on $\lambda$-bounded sequences for the logarithmic summability method with help of general logarithmic control modulo of the oscillatory behavior. Tauber conditions in our main results are on the generator sequence and the general logarithmic control modulo.

Keywords

Tauberian remainder theorem, $\lambda$-bounded sequence, logarithmic summability method, logarithmic general control modulo

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