, Volume 23, Issue 1, pp 55–73 | Cite as

Tauberian theorems for the logarithmic summability methods of integrals

  • Muhammet Ali OkurEmail author
  • Ümit Totur


A real-valued continuous function f on \([1, \infty )\) is said to be summable by the logarithmic summability method of integrals (shortly, \(\ell \) summable) if
$$\begin{aligned} \lim _{x \rightarrow \infty }\frac{1}{\log {x}}\int _1^x\frac{s(t)}{t}dt \end{aligned}$$
exists, where \(s(x)=\int _{1}^{x}f(t)dt\). Our goal in this paper is to obtain some Tauberian theorems for the logarithmic summability method of integrals by some new Tauberian conditions. We also introduce the \(\ell ^{(k)}\) summability method of integrals and give some Tauberian theorems for this method.


Tauberian theorem Tauberian condition Logarithmic summability method of integrals General control modulo 

Mathematics Subject Classification

Primary 40E05 Secondary 40A10 40C10 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsAdnan Menderes UniversityAydınTurkey
  2. 2.Sena SitesiAydınTurkey

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