We have established the estimation of deviation of continuous $$$2\pi$$$-periodic function $$$f(x)$$$ from the trigonometric polynomial of S.N. Bernstein's type that corresponds to it, by the modulus of continuity of the function $$$f(x)$$$.Встановлено оцінку відхилення неперервної $$$2\pi$$$-періодичної функції $$$f(x)$$$ від відповідного їй тригонометричного полінома типу С.Н. Бернштейна через модуль неперервності функції $$$f(x)$$$
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We prove sharp inequalities of various metrics for the norms $$$\| x \|_{p, \delta}$$$ of differenti...
For non-periodic functions $$$x \in L^r_{\infty}(\mathbb{R})$$$ defined on the whole real line we es...
We present the generalization of M.I. Chernykh's results about the estimate of the best $$$L_2$$$-ap...
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oai:ojs.vestnmath.dnu.dp.ua:article/292On one method of approximation of continuous periodic functio...
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Order estimates of deviation for special rational operators in integral and uniform metric of space ...
We prove sharp inequalities of various metrics for the norms $$$\| x \|_{p, \delta}$$$ of differenti...
For non-periodic functions $$$x \in L^r_{\infty}(\mathbb{R})$$$ defined on the whole real line we es...
We present the generalization of M.I. Chernykh's results about the estimate of the best $$$L_2$$$-ap...
Estimate of error of cubature formula for the class of differentiable $$$2\pi$$$-periodic functions ...
oai:ojs.vestnmath.dnu.dp.ua:article/292On one method of approximation of continuous periodic functio...
In the paper, we have found order asymptotic estimates of approximations, in the strong sense, relat...
We find the exact weak widths for one class of $$$2\pi$$$-periodic functions with values in Hilbert ...
We found the optimal information and the optimal method of its use to recover the convolution of n-f...
New sharp Bernstein type inequalities of different metrics in spaces of integrable functions for non...
We obtain certain inequalities of Jackson type, connecting the value of the best approximation of pe...
We received both upper and lower estimates as well as exact values of mutual deviation of certain in...
We point out that$$\inf\limits_{L \in L_n} \sup\limits_{\substack{f \in C_{2\pi}\\f \ne const}} \fra...
We solve the problem of optimization of approximate integration for the classes of periodic continuo...
For classes of $$$2\pi$$$-periodic functions of two discrete variables, defined on grid set $$$\sigm...
Order estimates of deviation for special rational operators in integral and uniform metric of space ...
We prove sharp inequalities of various metrics for the norms $$$\| x \|_{p, \delta}$$$ of differenti...
For non-periodic functions $$$x \in L^r_{\infty}(\mathbb{R})$$$ defined on the whole real line we es...