scholarly journals On Best Polynomial Approximations in the Spaces Sp and Widths of Some Classes of Functions

2016 ◽  
Vol 7 ◽  
pp. 19-32
Author(s):  
Alexander N. Shchitov
Keyword(s):  
Approximation Theory ◽  
Upper Bound ◽  
Special Form ◽  
Fourier Coefficients ◽  
Jackson Type ◽  
Polynomial Approximations

In the article are studied some problems of approximation theory in the spaces Sp (1 ≤ p < ∞) introduced by A.I. Stepanets. It is obtained the exact values of extremal characteristics of a special form which connect the values of best polynomial approximations of functions en-1(f)Sp with expressions which contain modules of continuity of functions f(x) є Sp. We have obtained the asymptotically sharp inequalities of Jackson type that connect the best polynomial approximations en-1(f)Sp with modules of continuity of functions f(x) є Sp (1 ≤ p < ∞). Exact values of Kolmogorov, linear, Bernstein, Gelfand and projection n-widths in the spaces Sp are obtained for some classes of functions f(x) є Sp. The upper bound of the Fourier coefficients are found for some classes of functions.

scholarly journals INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE

2020 ◽  
Vol 6 (2) ◽  
pp. 87
Author(s):  
Tatiana M. Nikiforova
Keyword(s):  
Approximation Theory ◽  
Upper Bound ◽  
Algebraic Polynomial ◽  
Uniform Norm ◽  
Algebraic Polynomials

The paper presents new solutions to two classical problems of approximation theory. The first problem is to find the polynomial that deviates least from zero on an ellipse. The second one is to find the exact upper bound of the uniform norm on an ellipse with foci \(\pm 1\) of the derivative of an algebraic polynomial with real coefficients normalized on the segment \([- 1,1]\).

Max-Product Shepard Approximation Operators

2006 ◽  
Vol 10 (4) ◽  
pp. 494-497 ◽  
Author(s):  
Barnabás Bede ◽  
◽  
Hajime Nobuhara ◽  
János Fodor ◽  
Kaoru Hirota ◽  
...  
Keyword(s):  
Error Estimate ◽  
Approximation Theory ◽  
Uniform Approximation ◽  
Approximation Theorem ◽  
Jackson Type ◽  
Approximation Operators

In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard approximation operators and we prove that these operators have very similar properties to those provided by the crisp approximation theory. In this sense we obtain uniform approximation theorem of Weierstrass type, and Jackson-type error estimate in approximation by these operators.

Approximations in several variables with freud-type and Ap-weights

2012 ◽  
Vol 49 (2) ◽  
pp. 139-155
Author(s):  
Nguyen Ky
Keyword(s):  
Jackson Type ◽  
Ap Weights ◽  
Polynomial Approximations ◽  
Several Variables

We present direct (Jackson-type) and converse (Bernstein-Stechkin-type) theorems for polynomial approximations with Freud-type weights and trigonometric approximations with Ap-weights, in the case of several variables.

Detecting Discontinuities from Fourier Coefficients Using Polynomial Approximations

2007 ◽  
Author(s):  
Alvaro R. De Pierro ◽  
Ana Gabriela Martínez ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Fourier Coefficients ◽  
Polynomial Approximations
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