Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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ISSN 2541-9005 (Online)

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Pleshakov M. G., Tyshkevich S. V. One counterexample of shape-preserving approximation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 2, pp. 144-150. DOI: 10.18500/1816-9791-2014-14-2-144-150, EDN: SHHIDL

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
09.06.2014
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.5
DOI: 
10.18500/1816-9791-2014-14-2-144-150
EDN: 
SHHIDL

One counterexample of shape-preserving approximation

Autors: 
Pleshakov Mixail Gennadevich, Saratov State University
Tyshkevich Sergey Viktorovich, Saratov State University
Abstract: 

Let 2s points yi=−π≤y2s

Key words: 
trigonometric polynomials
polynomial approximation
shape-preserving
References: 
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  2. Zygmund A. Smooth Functions. Duke Math. J., 1945, vol. 12, no. 1, pp. 47–76.
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  6. Dzyadyk V. K. O priblizhenii funktsii obyknovennymimnogochlenami na konechnom otrezke veshchestvennoi osi [On the approximation of functions by ordinary polynomials on a finite interval of the real axis]. Izvestiia AN SSSR. Ser. matematicheskaia, 1958, vol. 22, no. 3, pp. 337–354 (in Russian).
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  8. Teljakovskii S. A. Two theorems on approximation of functions by algebraic polynomials. Mat. Sb. (N. S.), 1966, vol. 70(112), no. 2, pp. 252–265 (in Russian).
  9. Brudnyi Yu. A. The approximation of functions by algebraic polynomials. Mathematics of the USSR-Izvestiya, 1968, vol. 2, no. 4, pp. 735–743. DOI: 10.1070/IM1968v002n04ABEH000662
  10. Lorentz G. G., Zeller K. L. Degree of Approximation by Monotone Polynomials. II. J. Approx. Theory, 1969, vol. 2, no. 3, pp. 265–269.
  11. Shevchuk I. A. Priblizhenie mnogochlenami i sledy nepreryvnykh na otrezke funktsii [Approximation by polynomials and traces continuous on the interval functions]. Kiev, Naukova dumka, 1992. 225 p. (in Russian)
  12. Shvedov A. S. Jackson’s theorem in Lp, 0 < p < 1, for algebraic polynomials, and orders of comonotone approximations. Math. Notes, 1979, vol. 25, no. 1, pp. 57–63.
  13. Shvedov A. S. Komonotonnoe priblizhenie funktsii mnogochlenami [Comonotone approximation of functions by polynomials]. Dokl. Akad. Nauk SSSR. 1980, vol. 250, no. 1, pp. 39–42 (in Russian).
  14. Dzyadyk V. K. Vvedenie v teoriiu ravnomernogo priblizheniia funktsii polinomami [Introduction to the theory of uniform approximation of functions by polynomials]. Moscow, Nauka, 1977, 512 p. (in Russian)
Received: 
19.11.2014
Accepted: 
20.04.2014
Published: 
30.05.2014
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