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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

- V. P. Motornyi
- Mathematics
- 30 June 1974

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

- V. P. Motornyi, O. V. Motornaya, P. K. Nitiema
- Mathematics
- 8 October 2010

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

- V. P. Motornyi
- Mathematics
- 1990

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, in… Expand

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Approximation of fractional-order integrals by algebraic polynomials. II

- V. P. Motornyi
- 1999

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

- V. P. Motornyi, A. N. Pas’ko
- Mathematics
- 17 November 2011

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

- V. P. Motornyi
- Mathematics
- 1991

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 the… Expand

On the Classification of Functions Integrable on a Segment

- O. V. Motornaya, V. P. Motornyi, V. V. Sedunova
- Mathematics
- 19 November 2016

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

- O. V. Motorna, V. P. Motornyi
- Mathematics
- 3 October 2019

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

- V. P. Motornyi
- Mathematics
- 1 March 2001

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 of… Expand

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On asymptotically exact estimates for the approximation of certain classes of functions by algebraic polynomials

- V. P. Motornyi, O. V. Motornaya
- Mathematics
- 2000

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 and… Expand

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