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Databases : Web of Science Core ... ✕Researcher : Fahreddin ABDULLAYEV ✕
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Prof. Dr. Fahreddin ABDULLAYEVFen Fakültesi
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Bernstein-Nikolskii-Markov-type inequalities for algebraic polynomials in a weighted Lebesgue space

Meerim İmaş Kızı | Fahreddin ABDULLAYEV

In this paper, we study Bernstein, Markov and Nikol’skii type inequalities for arbitrary algebraic polynomials with respect to a weighted Lebesgue space, where the contour and weight functions have some singularities on a given contour. Keyword: In this paper, we study Bernstein, Markov and Nikol’skii type inequalities for arbitrary algebraic polynomials with respect to a weighted Lebesgue space, where the contour and weight functions have some singularities on a given contour

Article 2023 Fen Fakültesi Filomat37 ( 17 ) 51 Views
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Fejér-type positive operator based on Takenaka-Malmquist system on unit circle

Fahreddin ABDULLAYEV

Let φ={φk}k=−∞∞ denote the extended Takenaka–Malmquist system on unit circle T and let σn,φ(f), f∈L1(T), be the Fejér-type operator based on φ, introduced by V. N. Rusak. We give the convergence criteria for σn,φ(f) in Banach space C(T). Also we prove the Voronovskaya-type theorem for σn,φ(f) on class of holomorphic functions representable by Cauchy-type integrals with bounded densities. Keywords: Holomorphic functions; Takenaka–Malmquist system; Fejér type operator; Blaschke product; Frostman condition

Article 2023 Fen Fakültesi Journal of Mathematical Analysis and Applications529 ( 2 ) 48 Views
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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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On the Sharp Inequalities for Orthonormal Polynomials Along a Contour

Fahreddin ABDULLAYEV

In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and the weight functions have some singularities. In particular, we obtain new exact estimations for the growth of the modulus of orthogonal polynomials

Article 2017 Fen Fakültesi Complex Analysis and Operator Theory11 ( 7 ) 89 Views
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Polynomial Inequalities in Quasidisks on Weighted Bergman Spaces

Fahreddin ABDULLAYEV

We continue studying on the Nikol’skii and Bernstein –Walsh type estimations for complex algebraic polynomials in the bounded and unbounded quasidisks on the weighted Bergman space

Article 2017 Fen Fakültesi Ukrainian Mathematical Journal69 ( 5 ) 88 Views
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Polynomial Inequalities in Regions with Corners in the Weighted Lebesgue Spaces

Fahreddin ABDULLAYEV

In this work, we investigate the order of the growth of the modulus of orthogonal polynomials over a contour and also arbitrary algebraic polynomials in regions with corners in a weighted Lebesgue space, where the singularities of contour and the weight functions satisfy some condition.

Article 2017 Fen Fakültesi Filomat31 ( 18 ) 40 Views
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The use of the isometry of function spaces with different numbers of variables in the theory of approximation of functions

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

In the work, we found integral representations for function spaces that are isometric to spaces of entire functions of exponential type, which are necessary for giving examples of equality of approximation characteristics in function spaces isometric to spaces of non-periodic functions. Sufficient conditions are obtained for the nonnegativity of the delta-like kernels used to construct isometric function spaces with various numbers of variables.

Article 2021 Fen Fakültesi Carpathian Mathematical Publications13 ( 3 ) 144 Views
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Bernstein-Walsh type inequalities for derivatives of algebraic polynomials in quasidisks

Fahreddin ABDULLAYEV

In this paper, we study Bernstein-Walsh type estimates for the higher-order derivatives of an arbitrary algebraic polynomial on quasidisks.

Article 2021 Fen Fakültesi Open Mathematics19 ( 1 ) 92 Views
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BERNSTEIN-WALSH TYPE INEQUALITIES FOR DERIVATIVES OF ALGEBRAIC POLYNOMIALS

Fahreddin ABDULLAYEV

In this work, we study Bernstein-Walsh-type estimations for the derivative of an arbitrary algebraic polynomial in regions with piece wise smooth boundary without cusps of the complex plane. Also, estimates are given on the whole complex plane.

Article 2022 Fen Fakültesi Bulletin of the Korean Mathematical Society (대한수학회보)59 ( 1 ) 21 Views
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On the growth of mth derivatives of algebraic polynomials in the weighted Lebesgue space

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

In this paper, we study the growth of the mth derivative of an arbitrary algebraic polynomial in bounded and unbounded general domains of the complex plane in weighted Lebesgue spaces. Further, we obtain estimates for the derivatives at the closure of this regions. As a result, estimates for derivatives on the entire complex plane were found.

Article 2022 Fen Fakültesi Applied Mathematics in Science and Engineering30 ( 1 ) 28 Views
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On the Growth of Derivatives of Algebraic Polynomials in a Weighted Lebesgue Space

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

We study the growth rates of the derivatives of an arbitrary algebraic polynomial in bounded and inbounded regions of the complex plane in weighted Lebesgue spaces.

Article 2022 Fen Fakültesi Ukrainian Mathematical Journal74 ( 5 ) 128 Views
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Bernstein-Walsh-type inequalities for derivatives of algebraic polynomials on the regions of complex plane

Fahreddin ABDULLAYEV

In this paper, we study Bernstein-Walsh-type estimates for the derivatives of an arbitrary algebraic polynomial on some general regions of the complex plane.

Article 2022 Fen Fakültesi Turkish Journal of Mathematics46 ( 7 ) 74 Views
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