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Index Type : Scopus ✕Subject Headings : best approximation ✕
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Best approximation-preserving operators over Hardy space

Fahreddin ABDULLAYEV

Let Tn be the linear Hadamard convolution operator acting over Hardy space Hq, 1≤q≤∞. We call Tn a best approximation-preserving operator (BAP operator) if Tn(en)=en, where en(z):=zn, and if ∥Tn(f)∥q≤En(f)q for all f∈Hq, where En(f)q is the best approximation by algebraic polynomials of degree a most n−1 in Hq space. We give necessary and sufficient conditions for Tn to be a BAP operator over H∞. We apply this result to establish an exact lower bound for the best approximation of bounded holomorphic functions. In particular, we show that the Landau-type inequality ∣∣fˆn∣∣+c∣∣fˆN∣∣≤En(f)∞, wher ...More

Article 2023 Fen Fakültesi Analysis and Mathematical Physics13 ( 4 ) 31 Views
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Best Approximation of Holomorphic Functions from Hardy Space in Terms of Taylor Coefficients

Fahreddin ABDULLAYEV

We describe the set of holomorphic functions from the Hardy space H-q, 1

Proceedings Paper 2019 Fen Fakültesi Filomat33 ( 5 ) 27 Views
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Direct and inverse approximation theorems of functions in the Orlicz type spaces S-M

Fahreddin ABDULLAYEV

In the Orlicz type spaces S-M, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre K-functionals in the spaces S-M. (C) 2019 Mathematical Institute Slovak Academy of Sciences

Article 2019 Fen Fakültesi Mathematica Slovaca69 ( 6 ) 60 Views
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Direct and inverse approximation theorems of functions in the Musielak-Orlicz type spaces

Fahreddin ABDULLAYEV

In Musilak-Orlicz type spaces S-M, direct and inverse approximation theorems are obtained in terms of the best approximations of functions and generalized moduli of smoothness. The question of the exact constants in Jackson-type inequalities is studied.

Article 2021 Fen Fakültesi Mathematical Inequalities & Applications24 ( 2 ) 38 Views
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Jackson-type inequalities and widths of functional classes in the Musielak–Orlicz type spaces

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

In the Musielak-Orlicz-type spaces S M , exact Jackson-type inequalities are obtained in terms of best approximations of functions and the averaged values of their generalized moduli of smoothness. The values of Kolmogorov, Bernstein, linear, and projective widths in SM are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.

Article 2021 Fen Fakültesi Rocky Mountain Journal of Mathematics51 ( 4 ) 115 Views
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Direct and inverse approximation theorems in the weighted Orlicz-type spaces with a variable exponent

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

In weighted Orlicz-type spaces S-p,S- (mu) with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre K-functionals is shown in the space ...More

Article 2020 Fen Fakültesi Turkish Journal of Mathematics44 ( 1 ) 37 Views
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