SOME INEQUALITIES BETWEEN THE BEST SIMULTANEOUS APPROXIMATION AND MODULUS OF CONTINUITY IN THE WEIGHTED BERGMAN SPACE
Some inequalities between the best simultaneous approximation of functions and their intermediate derivatives, and the modulus of continuity in a weighted Bergman space are obtained. When the weight function is \(\gamma(\rho)=\rho^\alpha,\) \(\alpha>0\), some sharp inequalities between the best s...
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| Format: | Article |
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2023-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/647 |
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| author | Muqim S. Saidusainov |
| author_facet | Muqim S. Saidusainov |
| author_sort | Muqim S. Saidusainov |
| collection | DOAJ |
| description | Some inequalities between the best simultaneous approximation of functions and their intermediate derivatives, and the modulus of continuity in a weighted Bergman space are obtained. When the weight function is \(\gamma(\rho)=\rho^\alpha,\) \(\alpha>0\), some sharp inequalities between the best simultaneous approximation and an \(m\)th order modulus of continuity averaged with the given weight are proved. For a specific class of functions, the upper bound of the best simultaneous approximation in the space \(B_{2,\gamma_{1}},\) \(\gamma_{1}(\rho)=\rho^{\alpha},\) \(\alpha>0\), is found. Exact values of several \(n\)-widths are calculated for the classes of functions \(W_{p}^{(r)}(\omega_{m},q)\). |
| format | Article |
| id | doaj-art-6aa426e0864d498fb2753a72273e35f2 |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-6aa426e0864d498fb2753a72273e35f22025-08-20T03:56:19ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522023-12-019210.15826/umj.2023.2.014191SOME INEQUALITIES BETWEEN THE BEST SIMULTANEOUS APPROXIMATION AND MODULUS OF CONTINUITY IN THE WEIGHTED BERGMAN SPACEMuqim S. Saidusainov0University of Central Asia, 55 Qimatsho Imatshoev, Khorog, GBAOSome inequalities between the best simultaneous approximation of functions and their intermediate derivatives, and the modulus of continuity in a weighted Bergman space are obtained. When the weight function is \(\gamma(\rho)=\rho^\alpha,\) \(\alpha>0\), some sharp inequalities between the best simultaneous approximation and an \(m\)th order modulus of continuity averaged with the given weight are proved. For a specific class of functions, the upper bound of the best simultaneous approximation in the space \(B_{2,\gamma_{1}},\) \(\gamma_{1}(\rho)=\rho^{\alpha},\) \(\alpha>0\), is found. Exact values of several \(n\)-widths are calculated for the classes of functions \(W_{p}^{(r)}(\omega_{m},q)\).https://umjuran.ru/index.php/umj/article/view/647the best simultaneous approximation, modulus of continuity, upper bound, \(n\)-widths |
| spellingShingle | Muqim S. Saidusainov SOME INEQUALITIES BETWEEN THE BEST SIMULTANEOUS APPROXIMATION AND MODULUS OF CONTINUITY IN THE WEIGHTED BERGMAN SPACE Ural Mathematical Journal the best simultaneous approximation, modulus of continuity, upper bound, \(n\)-widths |
| title | SOME INEQUALITIES BETWEEN THE BEST SIMULTANEOUS APPROXIMATION AND MODULUS OF CONTINUITY IN THE WEIGHTED BERGMAN SPACE |
| title_full | SOME INEQUALITIES BETWEEN THE BEST SIMULTANEOUS APPROXIMATION AND MODULUS OF CONTINUITY IN THE WEIGHTED BERGMAN SPACE |
| title_fullStr | SOME INEQUALITIES BETWEEN THE BEST SIMULTANEOUS APPROXIMATION AND MODULUS OF CONTINUITY IN THE WEIGHTED BERGMAN SPACE |
| title_full_unstemmed | SOME INEQUALITIES BETWEEN THE BEST SIMULTANEOUS APPROXIMATION AND MODULUS OF CONTINUITY IN THE WEIGHTED BERGMAN SPACE |
| title_short | SOME INEQUALITIES BETWEEN THE BEST SIMULTANEOUS APPROXIMATION AND MODULUS OF CONTINUITY IN THE WEIGHTED BERGMAN SPACE |
| title_sort | some inequalities between the best simultaneous approximation and modulus of continuity in the weighted bergman space |
| topic | the best simultaneous approximation, modulus of continuity, upper bound, \(n\)-widths |
| url | https://umjuran.ru/index.php/umj/article/view/647 |
| work_keys_str_mv | AT muqimssaidusainov someinequalitiesbetweenthebestsimultaneousapproximationandmodulusofcontinuityintheweightedbergmanspace |