Browsing by Author "Babich, Yurii P."

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Approximation of Periodic Functions of Many Variables by Functions of a Smaller Number of Variables in Orlicz Metric Spaces
(Springer, 2019) Babich, Yurii P.; Mikhailova, Tetiana F.
EN: For periodic functions of many variables, we propose a method for their approximation in the Orlicz spaces Lφ (T^m). According to this method, the functions are approximated by the sums of functions of smaller number of variables each of which is piecewise-constant in one variable for fixed values of the other variables. A Jackson-type inequality is analyzed for these approximations in terms of the mixed module of continuity.
Sharp Estimates for the Best Approximations of Smooth Functions in C 2π in Terms of Linear Combinations of the Modules of Continuity of Their Derivatives
(Ukrainian Mathematical Journal, Kyiv, 2022) Babich, Yurii P.; Mykhailova, Tetiana F.
ENG: For the best approximations of en-1(ƒ) functions from C12π by trigonometric polynomials, Zhuk earlier proved the exact Jackson inequality en-1(ƒ),,π/4n*ɷ(ƒ',π/n). This paper proves the following version of Jackson's exact inequality: en-1(ƒ),,π/4n*﴾(1/2ɷ(ƒ',π/2n)+1/2ɷ(ƒ',π/n)﴿.