Degree of Approximation of Functions by Nörlund Summability of Double Fourier Series
Year 2023,
Volume: 11 Issue: 2, 80 - 88, 30.06.2023
Suresh Kumar Sahani
,
Vishnu Narayan Mishra
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
Suresh Kumar Sahani
,
Vishnu Narayan Mishra
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).