Research Article
BibTex RIS Cite

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

Year 2023, Volume: 11 Issue: 2, 80 - 88, 30.06.2023

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].

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).
Year 2023, Volume: 11 Issue: 2, 80 - 88, 30.06.2023

Abstract

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).
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Suresh Kumar Sahani 0000-0002-3978-8734

Vishnu Narayan Mishra 0000-0002-2159-7710

Publication Date June 30, 2023
Submission Date October 12, 2021
Acceptance Date July 29, 2022
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

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 Sahani SK, Mishra VN. Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series. Math. Sci. Appl. E-Notes. June 2023;11(2):80-88. doi:10.36753/mathenot.1008750
Chicago 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 11, no. 2 (June 2023): 80-88. https://doi.org/10.36753/mathenot.1008750.
EndNote Sahani SK, 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 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, 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 2023), 80-88. https://doi.org/10.36753/mathenot.1008750.
JAMA Sahani SK, 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, 2023, pp. 80-88, doi:10.36753/mathenot.1008750.
Vancouver Sahani SK, Mishra VN. Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series. Math. Sci. Appl. E-Notes. 2023;11(2):80-8.

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.