Derivatives of polynomials of best approximation

We obtain the value of the best approximation of the linear combination, with non-negative coefficients, of the second partial derivatives and mixed derivatives of the second order on the class of multivariable functions with bounded third partial derivatives.

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Derivatives of a polynomial of best approximation and modulus of smoothness in generalized Lebesgue spaces with variable exponent

Demonstratio Mathematica ◽

10.1515/dema-2017-0023 ◽

2017 ◽

Vol 50 (1) ◽

pp. 245-251 ◽

Cited By ~ 2

Author(s):

Sadulla Z. Jafarov

Keyword(s):

Best Approximation ◽

Variable Exponent ◽

Modulus Of Smoothness ◽

Lebesgue Spaces ◽

The Best Approximation ◽

Polynomial Of Best Approximation ◽

The Relationship ◽

Derivatives Of ◽

De La Vallée Poussin

Abstract The relation between derivatives of a polynomial of best approximation and the best approximation of the function is investigated in generalized Lebesgue spaces with variable exponent. In addition, the relationship between the fractional modulus of smoothness of the function and its de la Vallée-Poussin sums is studied.

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Meansquare Approximation of Function Classes, Given on the all Real Axis R by the Entire Functions of Exponential Type

International Journal of Advanced Research in Mathematics ◽

10.18052/www.scipress.com/ijarm.6.1 ◽

2016 ◽

Vol 6 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Sergey B. Vakarchuk

Keyword(s):

Exponential Type ◽

Best Approximation ◽

Fractional Derivatives ◽

Entire Functions ◽

Weak Equivalence ◽

The Best Approximation ◽

Function Classes ◽

Functions Of Exponential Type ◽

Specific Restriction ◽

Derivatives Of

K-functionals K (f, t, L2(R), L2β(R), which defined by the fractional derivatives of order β>0, have been considered in the space L2(R). The relation K (f, tβ, L2(R), L2β(R) ≈ ωβ (f, t) (t>0) was obtained in the sense of the weak equivalence, where ωωβ (f, t) is the module of continuity of the fractional order β for a function f є L2(R). Exact values of the best approximation by entire functions of exponential type v∏, v є (0, ∞) have been computed for the classes of functions, given by the indicated K-functionals and majorants Ψ satisfying specific restriction. Kolmogorov, Bernsteinand linear mean v-widths were obtained for indicated classes of functions.

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Linear best method for recovering the second derivatives of Hardy class functions

E3S Web of Conferences ◽

10.1051/e3sconf/202016402013 ◽

2020 ◽

Vol 164 ◽

pp. 02013

Author(s):

Mikhail Ovchintsev

Keyword(s):

Finite Number ◽

Unit Circle ◽

Approximation Method ◽

Best Approximation ◽

Regular Polygon ◽

Extremal Functions ◽

Hardy Class ◽

The Third ◽

Second Derivatives ◽

Derivatives Of

The linear best method for approximating the second derivatives of Hardy class functions defined in the unit circle at zero in accordance with the information about their values in a finite number of points forming a regular polygon is found. The paper is divided into three sections. The first contains the necessary concepts and results from the work of K.Yu. Osipenko. It also recalls some results obtained by S. Ya. Havinson and other authors. In the second section, the error of the best method is calculated, and the corresponding extremal functions are written out. The third proves that the linear best approximation method is unique, and its coefficients are calculated.

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Trigonometric Approximation by Modulus of Smoothness in Lp,α (X)

Al-Mustansiriyah Journal of Science ◽

10.23851/mjs.v32i3.953 ◽

2021 ◽

Vol 32 (3) ◽

pp. 20

Author(s):

Mohammed Hamad Fayyadh ◽

Alaa Adnan Auad

Keyword(s):

Best Approximation ◽

Modulus Of Smoothness ◽

Trigonometric Approximation ◽

Weighted Spaces ◽

Trigonometric Polynomials ◽

The Best Approximation ◽

The Relationship ◽

Derivatives Of

In this paper, we study the approximate properties of functions by means of trigonometric polynomials in weighted spaces. Relationships between modulus of smoothness of function derivatives and those of the jobs themselves are introduced. In the weighted spaces we also proved of theorems about the relationship between the derivatives of the polynomials for the best approximation and the best approximation of the functions

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About the Optimal Recovery of Derivatives of Analytic Functions from Their Values at Points That Form a Regular Polygon

Mathematical Physics and Computer Simulation ◽

10.15688/mpcm.jvolsu.2019.4.2 ◽

2019 ◽

pp. 30-38

Author(s):

Mikhail Ovchintsev

Keyword(s):

Approximation Method ◽

Blaschke Product ◽

Analytic Functions ◽

Best Approximation ◽

Extremal Function ◽

Regular Polygon ◽

Optimal Recovery ◽

Bounded Analytic Functions ◽

The Best Approximation ◽

Derivatives Of

In this paper, the author solves the problem of optimal recovery of derivatives of bounded analytic functions defined at the zero of the unit circle. Recovery is performed based on information about the values of these functions at points z1, ... , zn , that form a regular polygon. The article consists of an introduction and two sections. The introduction talks about the necessary concepts and results from the works of Osipenko K.Yu. and Khavinson S.Ya., that form the basis for the solution of the problem. In the first section, the author proves some properties of the Blaschke product with zeros at the points z1, ... , zn. After this, the error of the best approximation method of the derivatives f(N)(0), 1 ≤ N ≤ n − 1, by the values f(z1), ... , f(zn) is calculated. In the same section he gives the corresponding extremal function. In the second section, the uniqueness of the linear best approximation method is established, and then its coefficients are calculated. At the end of the article, the formulas found for calculating of the coefficients are substantially simplified.

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