Estimation of deviation of continuous $$$2\pi$$$-periodic functions from corresponding trigonometric polynomials of S.N. Bernstein's type

N.Ya. Yatsenko (Dnipropetrovsk State University)

Abstract


We have established the estimation of deviation of continuous $$$2\pi$$$-periodic function $$$f(x)$$$ from the trigonometric polynomial of S.N. Bernstein's type that corresponds to it, by the modulus of continuity of the function $$$f(x)$$$.

References


Olovianishnikov V.M. "Estimation of remainder at approximation of continuous periodic functions by the polynomials that are the best in given point system", DAN SSSR, 1950; 70(5): pp. 761-764. (in Russian)

Bernstein S.N. Collection of works, vol. 2, Izd-vo AN SSSR, 1954. (in Russian)

Kish O. "On some interpolation processes of S.N. Bernstein", Acta Math. Acad. Sci. Hungar., 1973; 24(3-4): p. 353. (in Russian)




DOI: https://doi.org/10.15421/247712

  

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Copyright (c) 1977 N.Ya. Yatsenko

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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