Cite this article as:

Pleshakov M. ., Tyshkevich S. . One counterexample of shape-preserving approximation . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 2, pp. 144-150. DOI: https://doi.org/10.18500/1816-9791-2014-14-2-144-150

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.5

One counterexample of shape-preserving approximation

Authors: 
Pleshakov Mixail Gennadevich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , pleshakovmg@mail.ru
Tyshkevich Sergey Viktorovich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , tyszkiewicz@yandex.ru
Abstract: 

Let 2s points yi=−π≤y2s<… Example. For each k∈N, k>2, and n∈N there a function f(x):=f(x;s,Y,n,k) exists, such that f∈Δ(1)(Y) and
E(1)n(f;Y)>BYnk2−1ωk(f;1n),

where BY=const, depending only on Y and k; ωk is the modulus of smoothness of order k, of f.

Key words: 
trigonometric polynomials, polynomial approximation, shape-preserving.
DOI: 
https://doi.org/10.18500/1816-9791-2014-14-2-144-150
References
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