Fahreddin ABDULLAYEV

Article | 2019 | Mathematica Slovaca69 ( 6 )

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

Fahreddin ABDULLAYEV

Article | 2017 | Filomat31 ( 18 )

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.

Fahreddin ABDULLAYEV

Article | 2022 | Bulletin of the Korean Mathematical Society (대한수학회보)59 ( 1 )

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.

Sebahattin BALCI | Meerim İmaş Kızı | Fahreddin ABDULLAYEV

Article | 2018 | Ukrainian Mathematical Journal70 ( 3 )

We study the order of growth of the moduli of arbitrary algebraic polynomials in the weighted Bergman space A(p)(G, h), p > 0, in regions with zero interior angles at finitely many boundary points. We obtain estimates for algebraic polynomials in bounded regions with piecewise smooth boundary.

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

Article | 2022 | Applied Mathematics in Science and Engineering30 ( 1 )

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.

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

Article | 2020 | Ukrainian Mathematical Journal71 ( 8 )

We determine the subspaces of solutions of the systems of Laplace and heat-conduction differential equations isometric to the corresponding spaces of real functions defined on the set of real numbers.

Fahreddin ABDULLAYEV

Article | 2016 | Publications de l’Institut Mathématique100 ( 114 )

We study estimation of the modulus of algebraic polynomials in the bounded and unbounded regions with piecewise-quasismooth boundary, having interior and exterior zero angles, in the weighted Lebesgue space.

Fahreddin ABDULLAYEV

Article | 2020 | Ukrainian Mathematical Journal72 ( 1 )

We study the problem of approximation of functions (psi, beta)-differentiable (in the Stepanets sense) whose (psi, beta)-derivative belongs to the class H-alpha by biharmonic Poisson integrals in the uniform metric.

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

Article | 2020 | Quaestiones Mathematicae44 ( 10 )

In this paper, we study the uniform convergence ofp-Bieberbach polynomials in regions with a finite number of both interior and exterior zero angles at the boundary.

Fahreddin ABDULLAYEV

Proceedings Paper | 2019 | Filomat33 ( 2 )

In this study, we give some estimates on the Nikolskii-type inequalities for complex algebraic polynomials in regions with piecewise smooth curves having exterior and interior zero angles.

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

Article | 2020 | Turkish Journal of Mathematics44 ( 1 )

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 spaces S-p,S- (mu).

Fahreddin ABDULLAYEV

Article | 2017 | Complex Analysis and Operator Theory11 ( 7 )

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