A new extension on the theorem of Bor

Şebnem Yıldız

doi:10.5802/crmath.195

Numerical analysis

A new extension on the theorem of Bor

Şebnem Yıldız ¹

¹ Department of Mathematics, Ahi Evran University, Kırşehir, Turkey

Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 555-562.

Abstract

In [8], Bor has obtained a main theorem dealing with Riesz summability factors of infinite series and Fourier series. In this paper, we generalized that theorem to $| A, θ_{n} |_{k}$ summability method for taking power increasing sequence. Also some new and known results are obtained dealing with some basic summability methods.

Received: 2020-10-10
Revised: 2020-11-26
Accepted: 2021-03-01
Published online: 2021-07-13

DOI: 10.5802/crmath.195

Classification: 26D15, 42A24, 40F05, 40G99

Author's affiliations:

Şebnem Yıldız ¹

¹ Department of Mathematics, Ahi Evran University, Kırşehir, Turkey

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@article{CRMATH_2021__359_5_555_0,
     author = {\c{S}ebnem Y{\i}ld{\i}z},
     title = {A new extension on the theorem of {Bor}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {555--562},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {5},
     year = {2021},
     doi = {10.5802/crmath.195},
     language = {en},
}

TY  - JOUR
AU  - Şebnem Yıldız
TI  - A new extension on the theorem of Bor
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 555
EP  - 562
VL  - 359
IS  - 5
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.195
LA  - en
ID  - CRMATH_2021__359_5_555_0
ER  -

%0 Journal Article
%A Şebnem Yıldız
%T A new extension on the theorem of Bor
%J Comptes Rendus. Mathématique
%D 2021
%P 555-562
%V 359
%N 5
%I Académie des sciences, Paris
%R 10.5802/crmath.195
%G en
%F CRMATH_2021__359_5_555_0

Şebnem Yıldız. A new extension on the theorem of Bor. Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 555-562. doi : 10.5802/crmath.195. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.195/

References
Cited by

[1] Nina K. Bari; Sergeĭ B. Stechkin Best approximation and differential of two conjugate functions, Tr. Mosk. Mat. O.-va, Volume 5 (1956), pp. 483-522 (in Russian) | MR

[2] Hüseyin Bor On two summability methods, Math. Proc. Camb. Philos. Soc., Volume 97 (1985), pp. 147-149 | MR | Zbl

[3] Hüseyin Bor On the relative strength of two absolute summability methods, Proc. Am. Math. Soc., Volume 113 (1991), pp. 1009-1012 | MR | Zbl

[4] Hüseyin Bor Quasimonotone and almost increasing sequences and their new applications, Abstr. Appl. Anal., Volume 2012 (2012), 793548, 6 pages | MR | Zbl

[5] Hüseyin Bor On absolute weighted mean summability of infinite series and Fourier series, Filomat, Volume 30 (2016) no. 10, pp. 2803-2807 | MR | Zbl

[6] Hüseyin Bor Some new results on absolute Riesz summability of infinite series and Fourier series, Positivity, Volume 20 (2016) no. 3, pp. 599-605 | MR | Zbl

[7] Hüseyin Bor An application of quasi-monotone sequences to infinite series and Fourier series, Anal. Math. Phys., Volume 8 (2018) no. 1, pp. 77-83 | MR | Zbl

[8] Hüseyin Bor On absolute Riesz summability factors of infinite series and their aplication to Fourier series, Georgian Math. J., Volume 26 (2019) no. 3, pp. 361-366 | Zbl

[9] Ernesto Cesàro Sur la multiplication des sèries, Bull. Sci. Math., Volume 14 (1890), pp. 114-120 | Zbl

[10] Kien-Kwong Chen Functions of bounded variation and the Cesàro means of Fourier series, Acad. Sinica Sci. Record, Volume 1 (1945), pp. 283-289 | Zbl

[11] Thomas M. Flett On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. Lond. Math. Soc., Volume 7 (1957), pp. 113-141 | DOI | MR | Zbl

[12] Godfrey H. Hardy Divergent Series, Clarendon Press, 1949 | Zbl

[13] E. Kogbetliantz Sur lès series absolument sommables par la methode des moyennes arithmetiques, Bull. Sci. Math., Volume 49 (1925), p. 234--256 | Zbl

[14] J. O. Lee On the summability of infinite series and Hüseyin Bor, J. Hist. Math., Volume 30 (2017), pp. 353-365 (in Korean)

[15] László Leindler A new application of quasi power increasing sequences, Publ. Math., Volume 58 (2001) no. 4, pp. 791-796 | MR

[16] Hikmet S. Özarslan; T. Kandefer On the relative strength of two absolute summability methods, J. Comput. Anal. Appl., Volume 11 (2009) no. 3, pp. 576-583 | MR | Zbl

[17] Mehmet Ali Sarıgöl On the local properties of factored Fourier series, Math. Comp., Volume 216 (2010) no. 11, pp. 3386-3390 | MR | Zbl

[18] Waadallah T. Sulaiman On some summability factors of infinite series, Proc. Am. Math. Soc., Volume 115 (1992) no. 5, pp. 313-317 | DOI | MR

[19] Waadallah T. Sulaiman Inclusion theorems for absolute matrix summability methods of an infinite series, IV, Indian J. Pure Appl. Math., Volume 34 (2003) no. 11, pp. 1547-1557 | MR | Zbl

[20] Waadallah T. Sulaiman Extension on absolute summability factors of infinite series, J. Math. Anal. Appl., Volume 322 (2006) no. 2, pp. 1224-1230 | DOI | MR

[21] Waadallah T. Sulaiman Some new factor theorem for absolute summability, Demonstr. Math., Volume 46 (2013) no. 1, pp. 149-156 | MR | Zbl

[22] Şebnem Yıldız On application of matrix summability to Fourier series, Math. Methods Appl. Sci., Volume 41 (2018) no. 2, pp. 664-670 | MR | Zbl

[23] Şebnem Yıldız An absolute matrix summability of infinite series and Fourier series, Bol. Soc. Parana. Mat., Volume 38 (2020) no. 7, pp. 49-58 | DOI | MR | Zbl

Cited by Sources:

Comments - Policy