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The Span of the Translations of a Function in a Lebesgue Space. [PDF]

Proc Natl Acad Sci U S A, 1944
Segal IE.
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On Laguerre's Series: Third Note. [PDF]

Proc Natl Acad Sci U S A, 1926
Hille E.
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Tauberian conditions for absolute convergence

, 1973
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Remarks to some Tauberian conditions of mean type

Remarks to some Tauberian conditions of mean type
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Applications of Tauberian theorems for double sequences of fuzzy numbers via De La Vallée Poussin mean

Journal of Intelligent & Fuzzy Systems, 2021
Tauberian theorem serves the purpose to recuperate Pringsheim’s convergence of a double sequence from its (C, 1, 1) summability under some additional conditions known as Tauberian conditions.
A. Choudhary, K. Raj, M. Mursaleen
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Hardy-Type Tauberian Conditions on Time Scales

Mediterranean Journal of Mathematics, 2018
The authors obtain analogues of classical-type Tauberian conditions due to \textit{G. H. Hardy} [Proc. Lond. Math. Soc. (2) 8, 301--320 (1910; JFM 41.0278.02)] and \textit{R. Schmidt} [Math. Z. 22, 89--152 (1925; JFM 51.0182.04)] for the Cesàro summability of functions on time scales.
Yalçın, Ceylan Turan, Duman, Oktay
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Tauberian theorems and statistical Cesàro summability in the framework of neutrosophic normed spaces

Filomat
This paper establishes Tauberian theorems for statistical Ces?ro summability in neutrosophic normed spaces. We prove that q-bounded sequences statistically convergent under the neutrosophic norm (A, B, C) are also statistically Ces?ro summable, and ...
Mohamed Faisal, Mohd Kamran
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Tauberian conditions for the $$(C, \alpha )$$ ( C , α ) integrability of functions

Positivity, 2016
Let \(f(x)\) be a real-valued continuous function on \([0,\infty)\) and \(\displaystyle s(x)=\int_0^x f(u)du\). We set \[ \sigma_\alpha^x=\int_0^x\left(1-{u\over x}\right)^\alpha f(u)du, \] where \(\alpha>-1\). An improper integral \[ \int_0^\infty f(x)dx \] is said to be \((C, \alpha)\) integrable to \(L\) for some \(\alpha>-1\) if \[ \lim_{x\to\infty}
Ümit Totur, İbrahim Çanak
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Tauberian conditions for almost convergence

Positivity, 2008
Let \((X,\|.\|)\) denote a Banach space and let \(\Im =t\{ f_{i},i\geq 0\} \) denote a sequence in \(X\). The de la Vallée-Poussin mean and the Cesàro mean are defined as \(V_{n,N}(\Im )=\frac{1 }{N}\sum_{k=n}^{n+N-1}f_{k}\) and \(\sigma _{n}(\Im )=V_{0,n+1}(\Im )\). The authors consider the following limit statements. In each case \(f\in X\).
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On Tauberian Conditions for the Logarithmic Methods of Integrability

Bulletin of the Malaysian Mathematical Sciences Society, 2016
The authors obtain some new Tauberian conditions for the logarithmic integrability method. Furthermore, they introduce the logarithmic method of integrability of order two and then give Abel and Tauberian theorems for this method.
Totur, Ümit, Okur, Muhammet Ali
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