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Relevant bibliographies by topics / Tauberian theorems ; Oscillations

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Academic literature on the topic 'Tauberian theorems ; Oscillations'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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Journal articles on the topic "Tauberian theorems ; Oscillations"

1

Choudhary, Anu, Kuldip Raj, and M. Mursaleen. "Applications of Tauberian theorems for double sequences of fuzzy numbers via De La Vallée Poussin mean." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 11799–808. http://dx.doi.org/10.3233/jifs-202921.

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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. In this article, we intend to introduce some Tauberian theorems for fuzzy number sequences by using the de la Vallée Poussin mean and double difference operator of order r . We prove that a bounded double sequence of fuzzy number which is Δ u r - convergent is ( C , 1 , 1 ) Δ u r - summable to the same fuzzy number L . We make an effort to develop some new slowly oscillating and Hardy-type Tauberian condi

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2

GUL, ERDAL, and MEHMET ALBAYRAK. "Abel extensions of some classical Tauberian theorems." Creative Mathematics and Informatics 28, no. 2 (2019): 105–12. http://dx.doi.org/10.37193/cmi.2019.02.02.

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The well-known classical Tauberian theorems given for Aλ (the discrete Abel mean) by Armitage and Maddox in [Armitage, H. D and Maddox, J. I., Discrete Abel means, Analysis, 10 (1990), 177–186] is generalized. Similarly the ”one-sided” Tauberian theorems of Landau and Schmidt for the Abel method are extended by replacing lim As with Abel-lim Aσi n(s). Slowly oscillating of {sn} is a Tauberian condition of the Hardy-Littlewood Tauberian theorem for Borel summability which is also given by replacing limt(Bs)t = `, where t is a continuous parameter, with limn(Bs)n = `, and further replacing it by

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3

Parida, P., S. K. Paikray, Hemen Dutta, B. B. Jena, and M. Dash. "Tauberian theorems for Cesàro summability of nth sequences." Filomat 32, no. 11 (2018): 3993–4004. http://dx.doi.org/10.2298/fil1811993p.

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Tauberian theorem provides a criterion for the convergence of non convergent (summable) sequences. In this paper, we established a Tauberian theorem for nth real sequences via Ces?ro summability by using de la Vall?e Poussin mean and slow oscillation. The discussion and findings are capable to unify several useful concepts in the literature, and should also provide nontrivial extension of several results. Some examples are incorporated in support of our definitions and results. The findings are further expected to be helpful in designing and study several other interesting problems in summabil

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4

Parida, P., S. K. Paikray, and B. B. Jena. "Statistical Tauberian theorems for Cesàro integrability mean based on post-quantum calculus." Arabian Journal of Mathematics 9, no. 3 (2020): 653–63. http://dx.doi.org/10.1007/s40065-020-00284-z.

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Abstract The notion of statistical convergence is more general than the classical convergence. Tauberian theorems via different ordinary summability means have been established by many researchers. In the present work, we have established some new Tauberian theorems based on post-quantum calculus via statistical Cesàro summability mean of real-valued continuous function of one variable under oscillating behavior and De la vallée Poussin mean of a single integral. Moreover, some remarks and corollaries are provided here to support our theorems.

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5

Maddox, I. J. "A Tauberian theorem for statistical convergence." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 2 (1989): 277–80. http://dx.doi.org/10.1017/s0305004100078105.

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The notion of statistical convergence of a sequence (xk) in a locally convex Hausdorff topological linear space X was introduced recently by Maddox[5], where it was shown that the slow oscillation of (sk) was a Tauberian condition for the statistical convergence of (sk).

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6

Móricz, Ferenc, and Ulrich Stadtmüller. "Necessary and sufficient conditions under which convergence follows from summability by weighted means." International Journal of Mathematics and Mathematical Sciences 27, no. 7 (2001): 399–406. http://dx.doi.org/10.1155/s0161171201006688.

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We prove necessary and sufficient Tauberian conditions for sequences summable by weighted mean methods. The main results of this paper apply to all weighted mean methods and unify the results known in the literature for particular methods. Among others, the conditions in our theorems are easy consequences of the slowly decreasing condition for real numbers, or slowly oscillating condition for complex numbers. Therefore, practically all classical (one-sided as well as two-sided) Tauberian conditions for weighted mean methods are corollaries of our two main theorems.

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7

Çanak, Ibrahim, and Ümit Totur. "A Tauberian Theorem with a Generalized One-Sided Condition." Abstract and Applied Analysis 2007 (2007): 1–12. http://dx.doi.org/10.1155/2007/60360.

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We prove a Tauberian theorem to recover moderate oscillation of a real sequenceu=(un)out of Abel limitability of the sequence(Vn(1)(Δu))and some additional condition on the general control modulo of oscillatory behavior of integer order ofu=(un).

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8

Önder, Zerrin, and İbrahim Çanak. "Convergence follows from Cesàro summability in the case of slowly decreasing or slowly oscillating double sequences in certain senses." Filomat 34, no. 13 (2020): 4489–511. http://dx.doi.org/10.2298/fil2013489o.

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Let (u??) be a double sequence of real or complex numbers which is (C; 1; 1) summable to a finite limit. We obtain some Tauberian conditions of slow decreasing or oscillating types in terms of the generator sequences in certain senses under which P-convergence of a double sequence (u??) follows from its (C,1,1) summability. We give Tauberian theorems in which Tauberian conditions are of Hardy and Landau types as special cases of our results. We present some Tauberian conditions in terms of the de la Vall?e Poussin means of double sequences under which P-convergence of a double sequence (u??) f

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9

Bhowmik, Gautami, Olivier Ramaré, and Jan-Christoph Schlage-Puchta. "Tauberian Oscillation Theorems and the Distribution of Goldbach numbers." Journal de Théorie des Nombres de Bordeaux 28, no. 2 (2016): 291–99. http://dx.doi.org/10.5802/jtnb.940.

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10

Jena, Bidu Bhusan, Susanta Kumar Paikray, and Umakanta Misra. "A Tauberian Theorem for Double Cesàro Summability Method." International Journal of Mathematics and Mathematical Sciences 2016 (2016): 1–4. http://dx.doi.org/10.1155/2016/2431010.

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We have generalized Littlewood Tauberian theorems for(C,k,r)summability of double sequences by using oscillating behavior and de la Vallée-Poussin mean. Further, the generalization of(C,r)summability from(C,k,r)summability is given as corollaries which were earlier established by the authors.

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