In this work, the extremal function of the error functional in the Sobolev space of complex-valued functions is derived. Using the obtained extremal function, the squared norm of the error functional of quadrature formulas is computed. By minimizing the squared norm of the error functional with respect to the coefficients of the quadrature formulas, a system is derived for determining the optimal coefficients of the considered quadrature formula in the Sobolev space. In addition, an analogue of I. Babu\v{s}ka's theorem is proved.
| Mualliflar | Shadimetov , Kh. M., Tursunmurodov , S.T. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-11-03 |
| Jild | 69 |
| Son | 4 |
| Betlar | 194-200 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-4-19 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-4-19 · Maqolaning asl sahifasi
Extremal function, error functional, Sobolev space, quadrature formula, optimal coefficient
| APA | Shadimetov , Kh. M., & Tursunmurodov , S.T. (2025). Optimal quadrature formulas in the Sobolev space of complex-valued functions. O‘zbekiston matematika jurnali, 69(4), 194-200. https://doi.org/10.29229/uzmj.2025-4-19 |
|---|---|
| GOST (OAK) | Shadimetov , Kh. M., Tursunmurodov , S.T. Optimal quadrature formulas in the Sobolev space of complex-valued functions // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 4. – P. 194-200. – DOI: 10.29229/uzmj.2025-4-19. |
| MLA | Shadimetov , Kh. M., and Tursunmurodov , S.T. “Optimal quadrature formulas in the Sobolev space of complex-valued functions.” O‘zbekiston matematika jurnali, 69(4), 194-200, 2025. https://doi.org/10.29229/uzmj.2025-4-19 |
| Chicago | Shadimetov , Kh. M., and Tursunmurodov , S.T. “Optimal quadrature formulas in the Sobolev space of complex-valued functions.” O‘zbekiston matematika jurnali, 69(4), 194-200 (2025). https://doi.org/10.29229/uzmj.2025-4-19 |
| Harvard | Shadimetov , Kh. M., and Tursunmurodov , S.T (2025) ‘Optimal quadrature formulas in the Sobolev space of complex-valued functions’, O‘zbekiston matematika jurnali, 69(4), 194-200. https://doi.org/10.29229/uzmj.2025-4-19 |
| BibTeX | @article{shadimetovkhm2025,
title = {Optimal quadrature formulas in the Sobolev space of complex-valued functions},
author = {Shadimetov , Kh. M. and Tursunmurodov , S.T.},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {4},
pages = {194-200},
doi = {10.29229/uzmj.2025-4-19},
url = {https://doi.org/10.29229/uzmj.2025-4-19}
} |
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