
On the best polynomial approximation of $(\psi,\beta)$-differentiable functions in $L_2$ space
Author(s) -
С. Б. Вакарчук
Publication year - 2017
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241701
Subject(s) - differentiable function , beta (programming language) , mathematics , omega , polynomial , modulus of continuity , combinatorics , modulus , space (punctuation) , mathematical analysis , physics , type (biology) , geometry , quantum mechanics , computer science , programming language , ecology , linguistics , philosophy , biology
On the classes $L^{\psi}_{\beta,2}$ exact estimates have been obtained for the values of the best polynomial approximations of $(\psi,\beta)$-differentiable functions, expressed by the averages modulus of continuity $\widehat{\omega}(f^{\psi}_{\beta},t)$ with a weight $\xi(t)$. This modulus was introduced by K.V. Runovski and H.J. Schmeisser.