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Subsequential Convergence Conditions
Journal of Inequalities and Applications volume 2007, Article number: 087414 (2007)
Let be a sequence of real numbers and let be any regular limitable method. We prove that, under some assumptions, if a sequence or its generator sequence generated regularly by a sequence in a class of sequences is a subsequential convergence condition for, then for any integer, the repeated arithmetic means of,, generated regularly by a sequence in the class, is also a subsequential convergence condition for.
Stanojević ČV: Analysis of divergence: applications to the Tauberian theory, Graduate Research Seminar. University of Missouri-Rolla, Rolla, Mo, USA, 1999.
Stanojević ČV: Analysis of Divergence: Control and Management of Divergent Process, edited by İ. Çanak, Graduate Research Seminar Lecture Notes. University of Missouri-Rolla, Rolla, Mo, USA; 1998.
Hardy GH: Divergent Series. The Clarendon Press, Oxford University Press, New York, NY, USA; 1949:xvi+396.
Boos J: Classical and Modern Methods in Summability, Oxford Mathematical Monographs. Oxford University Press, Oxford, UK; 2000:xiv+586.
Dik M: Tauberian theorems for sequences with moderately oscillatory control modulo. Mathematica Moravica 2001, 5: 57–94.
Dik F: Tauberian theorems for convergence and subsequential convergence with moderately oscillatory behavior. Mathematica Moravica 2001, 5: 19–56.
Tauber A: Ein Satz aus der Theorie der unendlichen Reihen. Monatshefte für Mathematik und Physik 1897,8(1):273–277. 10.1007/BF01696278
Littlewood JE: The converse of Abel's theorem on power series. Proceedings of the London Mathematical Society 1911,9(2):434–448.
Rényi A: On a Tauberian theorem of O. Szász. Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum 1946, 11: 119–123.
Çanak İ, Totur Ü: Tauberian theorems for Abel limitability method. submitted for publication submitted for publication
Çanak İ: Tauberian theorems for a generalized Abelian summability methods. Mathematica Moravica 1998, 2: 21–66.
Çanak İ, Totur Ü: A note on Tauberian theorems for regularly generated sequences. submitted for publication submitted for publication
Çanak İ, Totur Ü: A Tauberian theorem with a generalized one-sided condition. Abstract and Applied Analysis 2007, 2007: 12 pages.
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Çanak, İ., Totur, Ü. & Dik, M. Subsequential Convergence Conditions. J Inequal Appl 2007, 087414 (2007). https://doi.org/10.1155/2007/87414
- Generator Sequence
- Real Number
- Convergence Condition
- Limitable Method
- Arithmetic Means