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ON THE BEST QUADRATURE FORMULA OF THE FORM $ \sum_{k=1}^np_kf(x_k)$ FOR SOME CLASSES OF DIFFERENTIABLE PERIODIC FUNCTIONS
We solve the problem of the best quadrature formula of the form for the following classes of differentiable periodic functions: , (where is a convex modulus of continuity and is odd), and .
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One-sided approximation of a step by algebraic polynomials in the mean
An asymptotically sharp estimate is obtained for the best one-sided approximation of a step by algebraic polynomials in the space L1:
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Investigation of the optimization of quadrature formulas by Dnepropetrovsk mathematicians
A survey of results is given on the extremal problems of the theory of quadratures, obtained by mathematicians whose scientific activity has been connected with the Dnepropetrovsk University and, inExpand
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Approximation of fractional-order integrals by algebraic polynomials. II
We investigate the approximation of functions that are fractional-order integrals of bounded functions by algebraic polynomials.
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Estimates for the best asymmetric approximations of asymmetric classes of functions
We obtain asymptotically sharp estimates for the best (α, β) -approximations of the classes $ W_{1;\upgamma, \updelta }^r $ with natural r by algebraic polynomials in the mean.
APPROXIMATION OF PERIODIC FIRqCTIONS BY INTERPOLATION POLYNOMIALS IN L
In the space ~ of continuous periodic functions [4] are given asymptotically precise estimates of the Lebesgue functions of interpolation polynomials ~(f; x) and lower bounds of the deviation at theExpand
On the Classification of Functions Integrable on a Segment
We study the problem of classification of functions integrable on a segment. Estimates for the integral moduli of continuity are obtained for functions from generalized Potapov’s classes.
On the Joint Approximation of a Function and its Derivatives in the Mean
We study the properties of functions integrable on a segment. Some estimates for the approximations of a function and its derivatives are obtained.
Approximation of Certain Classes of Singular Integrals by Algebraic Polynomials
We study the problem of pointwise approximation by algebraic polynomials for classes of functions that are singular integrals of bounded functions. We obtain asymptotically exact estimates ofExpand
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On asymptotically exact estimates for the approximation of certain classes of functions by algebraic polynomials
We present a survey of results obtained for the last decade in the field of approximation of specific functions and classes of functions by algebraic polynomials in the spaces C and L1 andExpand
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