@article{Shabozov_Akobirshoev_2020, title={Mean-square approximation by an angle in $L_2$ and the values of quasiwidths for some classes of functions}, volume={72}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/1064}, DOI={10.37863/umzh.v72i6.1064}, abstractNote={<p>UDC 517.5</p> <p>In the metric $L_{2},$ we obtain exact inequalities that associate the best approximations by trigonometrical ``angles’’ for functions $f(x,y),$ which are differentiable and $2\pi$-periodic in each variable, with the integrals containing modules of continuity of higher order for mixed derivatives of these functions.<span class="Apple-converted-space"> </span>For some classes of functions defined by modules of continuity, we calculate Kolmogorov’s quasiwidths and linear quasiwidths.</p>}, number={6}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Shabozov, M. Sh. and Akobirshoev , M. O.}, year={2020}, month={Jun.}, pages={852-864} }