Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series

Suresh Kumar Sahani; Vishnu Narayan Mishra

doi:10.36753/mathenot.1008750

EN

Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series

Abstract

In this research paper, the author studies some problems which are relating to harmonic summability of double Fourier series on Nörlund summability. These results constitute substantial extension and generalization of related works of F. Moricz and B.E Rhodes [1] and H.K. Nigam and K. Sharma [2].

Keywords

Nörlund sumambility, Double Fourier series;, Double Matrix summability

References

[1] Moricz, F., Rhodes, B. E.: Summablity of double Fourier series by Nörlund method at a point. Journal of Mathematical Analysis and Applications. 167, 203-215 (1992).
[2] Nigam, H. K., Sharma, K.: On the double summability of double conjugate Fourier series. International Journal of Mathematics and Mathematical Science. 2012, 104592 (2012).
[3] Sharma, P. L.: On the harmonic summability of double Fourier series. Proceeding of the American Mathematical Society. 9(6), 979-986 (1958).
[4] Tripathi L. M., Singh A. P.: A study of double Fourier series by Nörlund summability mathematics. Proceedings A. 84 (1), 139-143 (1981).
[5] Herriot J. G.: Nörlund summability of double Fourier series. Transactions of the American Mathematical Society. 52(1), 72-94 (1942).
[6] Lal, S., Tripathi, V. N.: On the study of double Fourier series by double matrix summability method. Tamkang Journal of Mathematics. 34(1), 1-16 (2003).
[7] Singh, T.: On the Nörlund summability of Fourier series and its conjugate series. Proc. Nat. Inst. Sci. India part A. 29, 65-73 (1963).
[8] Chow, Y. S.: On the Cesáro summability of double Fourier series. Tôhoku Math. J. 5, 277-283 (1953).
[9] Nuray, F., Ulusu, U., Dündar, E.: Cesàro summability of double sequence of sets. Gen. Math. Notes. 25(1), 8-18 (2014).
[10] Ulusu, U., Dündar, E., Gülle, E.: I-Cesáro summability of double sequence of sets. Palestine Journal of Mathematics. 9(1), 561-568 (2020).

[11] Ersoy, M. T., Furkan, H.: Distinguished supspaces in topological sequence spaces theory. Aims Mathematics. 5(4), 2858-2868 (2020).
[12] Cai, Q., Ansari, K. J., Ersoy, M. T., Özger, F.: Statistical blending-type approximation by a class of operators that includes shape parameters and . Mathematics. 10(7), 1149 (2022).
[13] Ersoy, M. T.: Some Abelian, Tauberian and Core theorems related to the V; summability. Universal Journal of Mathematics and Applications. 4(2), 70-75 (2021).
[14] Kama, R.: Spaces of vector sequences defined by the f-statistical convergence and some characterizations of normed spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales. Seria A. Matemáticas. 114, 74 (2020).
[15] Rama, R.: On some vector valued multiplier spaces with statistical Cesàro summability.Filomat. 33(16), 5135-5147 (2019).
[16] Moore, C. N.: Summability of series. The American Mathematical Monthly. 39(2), 62-71 (1932).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Suresh Kumar Sahani ^*
0000-0002-3978-8734
Nepal

Vishnu Narayan Mishra
0000-0002-2159-7710
India

Publication Date

June 30, 2023

Submission Date

October 12, 2021

Acceptance Date

July 29, 2022

Published in Issue

Year 2023 Volume: 11 Number: 2

DOI

https://doi.org/10.36753/mathenot.1008750

IZ

https://izlik.org/JA36NF95YW

APA

Sahani, S. K., & Mishra, V. N. (2023). Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series. Mathematical Sciences and Applications E-Notes, 11(2), 80-88. https://doi.org/10.36753/mathenot.1008750

AMA

1.Sahani S K, Mishra VN. Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series. Math. Sci. Appl. E-Notes. 2023;11(2):80-88. doi:10.36753/mathenot.1008750

Chicago

Sahani, Suresh Kumar, and Vishnu Narayan Mishra. 2023. “Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series”. Mathematical Sciences and Applications E-Notes 11 (2): 80-88. https://doi.org/10.36753/mathenot.1008750.

EndNote

Sahani S K, Mishra VN (June 1, 2023) Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series. Mathematical Sciences and Applications E-Notes 11 2 80–88.

IEEE

[1]S. K. Sahani and V. N. Mishra, “Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series”, Math. Sci. Appl. E-Notes, vol. 11, no. 2, pp. 80–88, June 2023, doi: 10.36753/mathenot.1008750.

ISNAD

Sahani, Suresh Kumar - Mishra, Vishnu Narayan. “Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series”. Mathematical Sciences and Applications E-Notes 11/2 (June 1, 2023): 80-88. https://doi.org/10.36753/mathenot.1008750.

JAMA

1.Sahani S K, Mishra VN. Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series. Math. Sci. Appl. E-Notes. 2023;11:80–88.

MLA

Sahani, Suresh Kumar, and Vishnu Narayan Mishra. “Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series”. Mathematical Sciences and Applications E-Notes, vol. 11, no. 2, June 2023, pp. 80-88, doi:10.36753/mathenot.1008750.

Vancouver

1.Suresh Kumar Sahani, Vishnu Narayan Mishra. Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series. Math. Sci. Appl. E-Notes. 2023 Jun. 1;11(2):80-8. doi:10.36753/mathenot.1008750