Degree of approximation by Fourier series in terms of the generalized modulus of smoothness
*Bushra Kadhum AwaadCorresponding authorbushra.k@uokerbala.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabylon, 51002, Iraq0009-0003-8224-5393View full profile → , Eman Samer Bhayaemanbhaya@alzahraa.edu.iqemanbhaya@itnet.uobabylon.edu.iqDepartment of MathematicsCollege of Education for Pure SciencesUniversity of BabylonBabylon, 51002, Iraq0000-0002-8241-6987View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Jun 2024
- Published Online:
- 13 Feb 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1799
- Pages:
- 89–93
Abstract
Keywords
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References
[1] P. Chandra, “On the degree of approximation of continuous functions,” Acta Math. Hungar., vol. 62, no. 1–2, pp. 21–23 (1993), https://doi.org/10.1007/bf01874214.
[2] Xh. Z. Krasniqi, “On the degree of approximation of continuous functions by a linear transformation of their Fourier series,” Communications in Mathematics, vol. 30 (2022).
[3] Z. Ditzian and V. Totik, Moduli of Smoothness, New York: Springer Verlag (1987).
[4] L. Leindler, “On the degree of approximation of continuous functions,” Acta Math. Hungar., vol. 104, no. 1-2, pp. 105-113 (2004).
[5] P. Chandra, “Trigonometric approximation of functions in Lp-norm,” J. Math. Anal. Appl., vol. 275, pp. 13–26 (2002).
[6] R. N. Mohapatra and D. C. Russell, “Some direct and inverse theorems in approximation of functions,” J. Austral. Math. Soc. Ser. A, vol. 34, pp. 143-154 (1983).
[7] Z. Ditzian and V. Totik, Moduli of Smoothness, New York: Springer-Verlag (1987).
[8] M. R. Farahani, S. Jafari, S. A. Mohiuddine, and M. Cancan, “Intuitionistic fuzzy stability of generalized additive set-valued functional equation via fixed point method,” Mathematical Statistician and Engineering Applications, vol. 71, no. 3s3, pp. 142-154 (2022). [Online]. Available: https://www.philstat.org.ph/index.php/MSEA/article/view/355.
[9] A.M. Darweesh, R.H. Hasan, and S.M. Kadham, “Results of Fourth-Order Differential Superordination and Subordination for Univalent Functions Defined by Integral Operator,” Mathematical Modelling and Engineering Problems, vol. 11, no. 2, pp. 385–392 (Feb. 2024), doi: https://doi.org/10.18280/mmep.110210.
[10] S. Kadham and A. Alkiffai, “Model Tumor Response to Cancer Treatment Using Fuzzy Partial SH-Transform: An Analytic Study,” International Journal of Mathematics and Computer Science, vol. 18, no. 1, pp. 23–28 (2022), Available: https://future-in-tech.net/18.
[11] S. M. Kadham and A. N. Alkiffai, “Generalization of Fuzzy SHA-Transform with Medical Application,” Mathematical Modelling of Engineering Problems, vol. 9, no. 5, pp. 1378–1384 (Dec. 2022), doi: https://doi.org/10.18280/mmep.090528.
[12] H. R. Hasan, M. A. Kadhim, and A. M. Darweesh, “Fuzzy partial T-transforms applied to a system of PDE,” J. Interdiscip. Math., vol. 26, no. 6, pp. 1099-1107 (2022). [Online]. Available: https://doi.org/10.47974/JIM-1609.
[13] S. Jafari, M. R. Farahani, and M. Rajesh, “Double fuzzy rarely continuous functions,” Annals of Fuzzy Mathematics and Informatics, vol. 26, no. 1, pp. 35-45 (2023).
[14] M. Nadeem, S. Ahmad, M. K. Siddiqui, M. A. Ali, M. R. Farahani, and A. J. M. Khalaf, “On some applications related with algebraic structures through different well-known graphs,” J. Discrete Math. Sci. Cryptography, vol. 24, no. 2, pp. 451-471 (2021). [Online]. Available: https://doi.org/10.1080/0972052.
[15] A. H. Alwan, “Small intersection graph of subsemimodules of a semi-module,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2022, no. 1, pp. 15-22 (2022).
[16] S. Ediz, M. Cancan, and M. R. Farahani, “Eccentric connectivity and connective eccentricity indices of generalized Petersen graphs,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2021, no. 1, pp. 1-6 (2021).
[17] R. Ponraj, S. Prabhu, and M. Sivakumar, “Pair mean cordial labeling of total graph of some graphs and prism-related graphs,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2024, no. 2, pp. 181-192 (2024).
[18] F. O. Oduol and I. O. Okoth, “Counting vertices among all noncrossing trees by levels and degrees,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2024, no. 2, pp. 193-212 (2024).
[19] A. Lebban, A. A. Alraie, Q. A. Jabal, A. Rasool, Rawa Shakir Muwashee, and W. H. Mahdi, “The effect of anti-slip aggregate and silica fume on polymer-modified concrete,” Pollack Periodica, vol. 19, no. 2, pp. 76–81 (Feb. 2024), doi: https://doi.org/10.1556/606.2023.00958.
[20] L. A. R. Al Asadi, H. S. Al Bahrani, and L. K. Al Waeli, “Parametric Study for Design and Analysis of Box Culvert by Using Newton’s-Raphson Method and MATLAB Software,” Key Engineering Materials, vol. 870, pp. 11–19 (Oct. 2020), doi: https://doi.org/10.4028/www.scientific.net/kem.870.11.
[21] S.N.J. Alamiry, S.M. Kadham, M. A. Mustafa, and N. K. Abbass, “Encryption and enhance medical image using hybrid transform (Ã-module and partial fuzzy Ȟ-transform),” J. Discrete Math. Sci. Cryptogr., vol. 26, no. 7, pp. 1903–1910 (2023), [Online]. Available https://doi.org/10.47974/jdmsc-1683.
