EN
On the Euler method of summability and concerning Tauberian theorems
Abstract
For any two regular summability methods (U) and (V), the condition under which V-limx_n=λ implies U-limx_n=λ is called a Tauberian condition and the corresponding theorem is called a Tauberian theorem. Usually in the theory of summability, the case in which the method U is equivalent to the ordinary convergence is taken into consideration. In this paper, we give new Tauberian conditions under which ordinary convergence or Cesàro summability of a sequence follows from its Euler summability by means of the product theorem of Knopp for the Euler and Cesàro summability methods.
Keywords
References
- [1] Hardy G.H., Divergent series. 1st ed. Oxford: Clarendon Press, (1949).
- [2] Meyer-König W., Zeller K., Kronecker-Ausdruck und Kreisverfahren der Limitierungstheorie, Math. Z., 114 (1970), 300-302.
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- [6] Çanak İ., Braha N.L., Totur Ü., A Tauberian Theorem for the Generalized Nörlund Summability Method, Georgian Math. J., 27 (2020), 31-36.
- [7] Sezer S.A., Çanak İ., Tauberian Conditions of Slowly Decreasing Type for the Logarithmic Power Series Method, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 90 (2020), 135-139.
- [8] Sezer S.A., Çanak İ, Tauberian Conditions under which Convergence follows from Summability by the Discrete Power Series Method, Turk. J. Math., 43 (2019), 2898-2907.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
March 29, 2021
Submission Date
December 1, 2020
Acceptance Date
March 17, 2021
Published in Issue
Year 2021 Volume: 42 Number: 1
APA
Sezer, S. A., & Çanak, İ. (2021). On the Euler method of summability and concerning Tauberian theorems. Cumhuriyet Science Journal, 42(1), 141-144. https://doi.org/10.17776/csj.834216
AMA
1.Sezer SA, Çanak İ. On the Euler method of summability and concerning Tauberian theorems. CSJ. 2021;42(1):141-144. doi:10.17776/csj.834216
Chicago
Sezer, Sefa Anıl, and İbrahim Çanak. 2021. “On the Euler Method of Summability and Concerning Tauberian Theorems”. Cumhuriyet Science Journal 42 (1): 141-44. https://doi.org/10.17776/csj.834216.
EndNote
Sezer SA, Çanak İ (March 1, 2021) On the Euler method of summability and concerning Tauberian theorems. Cumhuriyet Science Journal 42 1 141–144.
IEEE
[1]S. A. Sezer and İ. Çanak, “On the Euler method of summability and concerning Tauberian theorems”, CSJ, vol. 42, no. 1, pp. 141–144, Mar. 2021, doi: 10.17776/csj.834216.
ISNAD
Sezer, Sefa Anıl - Çanak, İbrahim. “On the Euler Method of Summability and Concerning Tauberian Theorems”. Cumhuriyet Science Journal 42/1 (March 1, 2021): 141-144. https://doi.org/10.17776/csj.834216.
JAMA
1.Sezer SA, Çanak İ. On the Euler method of summability and concerning Tauberian theorems. CSJ. 2021;42:141–144.
MLA
Sezer, Sefa Anıl, and İbrahim Çanak. “On the Euler Method of Summability and Concerning Tauberian Theorems”. Cumhuriyet Science Journal, vol. 42, no. 1, Mar. 2021, pp. 141-4, doi:10.17776/csj.834216.
Vancouver
1.Sefa Anıl Sezer, İbrahim Çanak. On the Euler method of summability and concerning Tauberian theorems. CSJ. 2021 Mar. 1;42(1):141-4. doi:10.17776/csj.834216