Geodesic
Some inequalities between the best simultaneous approximation and the modulus of continuity in a weighted Bergman space
Ural mathematical journal, Tome 9 (2023) no. 2, pp. 165-174

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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 $W_{p}^{(r)}(\omega_{m},q)$.
Keywords: The best simultaneous approximation, modulus of continuity, upper bound, $n$-widths. 
@article{UMJ_2023_9_2_a13,
     author = {Muqim S. Saidusajnov},
     title = {Some inequalities between the best simultaneous approximation and the modulus of continuity in a weighted {Bergman} space},
     journal = {Ural mathematical journal},
     pages = {165--174},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2023_9_2_a13/}
}
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Muqim S. Saidusajnov. Some inequalities between the best simultaneous approximation and the modulus of continuity in a weighted Bergman space. Ural mathematical journal, Tome 9 (2023) no. 2, pp. 165-174. http://geodesic.mathdoc.fr/item/UMJ_2023_9_2_a13/