Geodesic
Comparison of the best approximation of holomorphic functions from Hardy space
Abdullayev, F. G. 1 ; Savchuk, V. V. 2 ; Simsek, D. 3
1 Mersin University, Mersin, Turkey;Kyrgyz--Turkish Manas University, Bishkek, Kyrgyzstan
2 Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine
3 Kyrgyz--Turkish Manas University, Bishkek, Kyrgyzstan
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 7, p. 412-419.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We compare the best approximations of holomorphic functions in the Hardy space $H^1$ by algebraic polynomials and trigonometric polynomials. Particulary, we establish a class of functions $f\in H^1$ for which the best trigonometric approximation do not coincide with the best algebraic approximation.
DOI : 10.22436/jnsa.012.07.01
Classification : 30C45, 30C50
Keywords: Best approximation, Hardy space, non-negative trigonometric polynomials

Abdullayev, F. G.  1 ; Savchuk, V. V.  2 ; Simsek, D.  3

1 Mersin University, Mersin, Turkey;Kyrgyz--Turkish Manas University, Bishkek, Kyrgyzstan
2 Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine
3 Kyrgyz--Turkish Manas University, Bishkek, Kyrgyzstan 
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Abdullayev, F. G. ; Savchuk, V. V. ; Simsek, D. . Comparison of the best approximation of holomorphic functions from Hardy space. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 7, p. 412-419. doi : 10.22436/jnsa.012.07.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.07.01/

[1] Abdullayev, F. G.; Abdullayev, G. A.; Savchuk, V. V. Best approximation of holomorphic functions from Hardy space in terms of Taylor coefficient (to appear in Filomat.)

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[6] Savchuk, V. V.; Savchuk, M. V.; Chaichenko, S. O. Approximation of Analytic Functions byde Valle Poussin sums (Ukrainian), Matematychni Studii, Volume 34 (2010), pp. 207-219

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