A Tauberian theorem for the product of Abel and Cesàro summability methods
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Yılmaz Erdem
Abstract
In this paper, we prove a Tauberian theorem for the product of the Abel method and the Cesàro method of order α, which improves some classical Tauberian theorems for the Abel and Cesàro summability methods.
References
[1]
Abel N. H.,
Recherches sur la série
[2] Amir A., On a converse of Abel’s theorem, Proc. Amer. Math. Soc. 3 (1952), no. 2, 244–256. 10.1090/S0002-9939-1952-0047153-5Search in Google Scholar
[3] Boos J., Classical and Modern Methods in Summability, Oxford Math. Monogr., Oxford University Press, Oxford, 2000. 10.1093/oso/9780198501657.001.0001Search in Google Scholar
[4] Borwein D., Theorems on some methods of summability, Quart. J. Math. Oxford Ser. (2) 9 (1958), 310–316. 10.1093/qmath/9.1.310Search in Google Scholar
[5]
Çanak İ. and Erdem Y.,
On Tauberian theorems for
[6]
Çanak İ., Erdem Y. and Totur Ü.,
Some Tauberian theorems for
[7]
Erdem Y. and Çanak İ.,
A Tauberian theorem for
[8] Hardy G. H., Theorems relating to the summability and convergence of slowly oscillating series, Proc. Lond. Math. Soc. (2) 8 (1910), 301–320. 10.1112/plms/s2-8.1.301Search in Google Scholar
[9] Hardy G. H. and Littlewood J. E., Tauberian theorems concerning power and Dirichlet’s series whose coefficients are positive, Proc. Lond. Math. Soc. (2) 13 (1914), 174–191. 10.1112/plms/s2-13.1.174Search in Google Scholar
[10] Kogbetliantz E., Sur les séries absolument sommables par la méthode des moyennes arihtmétiques, Bulletin Sci. Math. (2) 49 (1925), 234–251. Search in Google Scholar
[11] Kogbetliantz E., Sommation des séries et intégrals divergents par les moyennes arithmétiques et typiques, Memorial Sci. Math. 51 (1931), 1–84. Search in Google Scholar
[12] Littlewood J. E., The converse of Abel’s theorem on power series, Proc. Lond. Math. Soc. (2) 9 (1911), 434–448. 10.1112/plms/s2-9.1.434Search in Google Scholar
[13] Lord R. D., On some relations between the Abel, Borel and Cesàro methods of summations, Proc. Lond. Math. Soc. (2) 38 (1935), no. 2, 241–246. 10.1112/plms/s2-38.1.241Search in Google Scholar
[14] Pati T., On Tauberian theorems, Sequences, Summability and Fourier Analysis, Narosa Publishing House, New Delhi (2005), 84–96. Search in Google Scholar
[15] Szàsz O., Generalization of two theorems of Hardy and Littlewood on power series, Duke Math. J. 1 (1935), no. 1, 105–111. 10.1215/S0012-7094-35-00111-9Search in Google Scholar
[16] Tauber A., Ein Satz der Theorie der unendlichen Reihen, Monatsh. Math. 8 (1897), 273–277. 10.1007/BF01696278Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Non-trivial solutions for nonlocal elliptic problems of Kirchhoff-type
- Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data
- On the modification of the Szaśz–Durrmeyer operators
- A spectral representation of the linear multivelocity transport problem
- A Tauberian theorem for the product of Abel and Cesàro summability methods
- The spaces of bilinear multipliers of weighted Lorentz type modulation spaces
- Summations of Schlömilch series containing Struve function terms
- On nondifferentiable minimax semi-infinite programming problems in complex spaces
- Modified relativistic Laguerre polynomials. Monomiality and Lie algebraic methods
- On the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector
- The Hardy--Littlewood maximal operator and BLO1/log class of exponents
- Bicritical domination and double coalescence of graphs
- The asymptotic behavior of a counting process in the max-scheme. A discrete case
- Functions of bounded fractional differential variation – A new concept
- Sensitivity analysis of the optimal exercise boundary of the American put option
- Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction
- A coupled system of nonlinear differential equations involving m nonlinear terms
Articles in the same Issue
- Frontmatter
- Non-trivial solutions for nonlocal elliptic problems of Kirchhoff-type
- Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data
- On the modification of the Szaśz–Durrmeyer operators
- A spectral representation of the linear multivelocity transport problem
- A Tauberian theorem for the product of Abel and Cesàro summability methods
- The spaces of bilinear multipliers of weighted Lorentz type modulation spaces
- Summations of Schlömilch series containing Struve function terms
- On nondifferentiable minimax semi-infinite programming problems in complex spaces
- Modified relativistic Laguerre polynomials. Monomiality and Lie algebraic methods
- On the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector
- The Hardy--Littlewood maximal operator and BLO1/log class of exponents
- Bicritical domination and double coalescence of graphs
- The asymptotic behavior of a counting process in the max-scheme. A discrete case
- Functions of bounded fractional differential variation – A new concept
- Sensitivity analysis of the optimal exercise boundary of the American put option
- Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction
- A coupled system of nonlinear differential equations involving m nonlinear terms
