commun. fac. sci. univ. ank. ser. a1 math. stat.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

1303-5991 2618-6470

Ankara University

10.31801/cfsuasmas.1380675

Pure Mathematics (Other)

Temel Matematik (Diğer)

General logarithmic control modulo and Tauberian remainder theorems

https://orcid.org/0000-0002-8352-2570

Okur

Muhammet Ali

ADNAN MENDERES UNIVERSITY

06 21 2024

73 2 391 398 10 25 2023 12 19 2023

1948

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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.

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

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