Avıt ASANOV

Article | 2020 | Ukrainian Mathematical Journal72 ( 2 )

On the basis of a new approach, we prove the uniqueness theorem and construct Lavrent'ev's regularizing operators for the solution of nonclassical linear Volterra integral equations of the first kind with nondifferentiable kernels.

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

Article | 2021 | Ukrainian Mathematical Journal73 ( 4 )

We study Bernstein-type and Nikol'skii-type estimates for an arbitrary algebraic polynomial in regions of the complex plane.

Fahreddin ABDULLAYEV

Article | 2017 | Ukrainian Mathematical Journal69 ( 5 )

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

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 | Meerim İmaş Kızı

Article | 2022 | Ukrainian Mathematical Journal74 ( 5 )

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.

Asan ÖMÜRALİEV | Ella ABILAYEVA

Article | 2022 | Ukrainian Mathematical Journal73 ( 12 )

The regularized asymptotics of the solution of the first boundary-value problem for a two-dimensional differential equation of parabolic type is constructed in the case where the phase derivative vanishes at a single point. It is shown that angular and multidimensional boundary-layer functions appear in problems of this kind parallel with other types of boundary layers.

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

Article | 2021 | Ukrainian Mathematical Journal737 ( 6 )

We obtain exact Jackson-type inequalities in terms of the best approximations and averaged values of the generalized moduli of smoothness in the spaces S-p. For classes of periodic functions defined by certain conditions imposed on the average values of the generalized moduli of smoothness, we determine the exact values of the Kolmogorov, Bernstein, linear, and projective widths in the spaces S-p.

Fahreddin ABDULLAYEV | Dağıstan ŞİMŞEK

Article | 2019 | Ukrainian Mathematical Journal71 ( 5 )

We continue our investigation of the order of growth of the modulus of an arbitrary algebraic polynomial in the Bergman weight space, where the contour and weight functions have certain singularities. In particular, we deduce a Bernstein-Walsh-type pointwise estimate for algebraic polynomials in unbounded domains with piecewise asymptotically conformal curves with nonzero inner angles in the Bergman weight space.

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

Article | 2018 | Ukrainian Mathematical Journal70 ( 2 )

We study the possibility of application of Faber polynomials in proving some combinatorial identities. It is shown that the coefficients of Faber polynomials of mutually inverse conformal mappings generate a pair of mutually invertible relations. We prove two identities relating the coefficients of Faber polynomials and the coefficients of Laurent expansions of the corresponding conformal mappings. Some examples are presented.