# Comparison of the best approximation of holomorphic functions from Hardy space

Volume 12, Issue 7, pp 412--419
Publication Date: March 08, 2019 Submission Date: October 22, 2018 Revision Date: January 18, 2019 Accteptance Date: January 25, 2019
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### Authors

F. G. Abdullayev - Mersin University, Mersin, Turkey. - Kyrgyz--Turkish Manas University, Bishkek, Kyrgyzstan. V. V. Savchuk - Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine. D. Simsek - Kyrgyz--Turkish Manas University, Bishkek, Kyrgyzstan.

### Abstract

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.

### Share and Cite

##### ISRP Style

F. G. Abdullayev, V. V. Savchuk, D. Simsek, Comparison of the best approximation of holomorphic functions from Hardy space, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 7, 412--419

##### AMA Style

Abdullayev F. G., Savchuk V. V., Simsek D., Comparison of the best approximation of holomorphic functions from Hardy space. J. Nonlinear Sci. Appl. (2019); 12(7):412--419

##### Chicago/Turabian Style

Abdullayev, F. G., Savchuk, V. V., Simsek, D.. "Comparison of the best approximation of holomorphic functions from Hardy space." Journal of Nonlinear Sciences and Applications, 12, no. 7 (2019): 412--419

### Keywords

• Best approximation
• Hardy space
• non-negative trigonometric polynomials

•  30C45
•  30C50

### References

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

• [2] S. Y. Al’per , On the Best Mean First-degree Approximation of Analytic Functions on Circle (Russian), Dokl. Akad. Nauk S.S.S.R., 153 (1963), 503–506.

• [3] A. A. Pekarskii, Comparison of the Best Uniform Approximations of Analytic Functions in the Disk and on Its Boundary (Russian), translated from Tr. Mat. Inst. Steklova, 255 (2006), 227–232.

• [4] V. V. Savchuk, Best Approximation of Cauchy–Szegö Kernel in the Mean on Circle (Ukrainian), Ukr. Mat. Zh., 70 (2018), 708–714

• [5] V. V. Savchuk, S. O. Chaichenko, Addendum to a theorem of F. Wiener about sieve (Ukrainian), Praci Instytutu Matematyky NAN Ukrainy, 12 (2015), 262–272.

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