Geodesic
Best restricted approximation of smooth function classes
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 283-294

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We first discuss the relative Kolmogorov $n$-widths of classes of smooth $2\pi$-periodic functions for which the modulus of continuity of their $r$-th derivatives does not exceed a given modulus of continuity, and then discuss the best restricted approximation of classes of smooth bounded functions defined on the real axis $\mathbb R$ such that the modulus of continuity of their $r$-th derivatives does not exceed a given modulus of continuity by taking the classes of the entire functions of exponential type as approximation tools. Asymptotic results are obtained for these two problems.
Keywords: modulus of continuity, best restricted approximation, average width. 
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     author = {Y. Liu and G. Xu and J. Zhang},
     title = {Best restricted approximation of smooth function classes},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {283--294},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a22/}
}
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Y. Liu; G. Xu; J. Zhang. Best restricted approximation of smooth function classes. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 4, pp. 283-294. http://geodesic.mathdoc.fr/item/TIMM_2018_24_4_a22/