Zhyhallo K. M.
On the approximation of functions from the Hölder class given on a segment by their biharmonic Poisson operators
Zhyhallo K. M., Zhyhallo T. V.
↓ Abstract
Ukr. Mat. Zh. - 2019. - 71, № 7. - pp. 915-921
UDC 517.5
We obtain the exact equality for the upper bounds of deviations of biharmonic Poisson operators on the Hölder classes of functions continuous on the segment $[-1;1]$.
Approximative properties of biharmonic Poisson integrals on Hölder classes
Hembars'ka S. B., Zhyhallo K. M.
Ukr. Mat. Zh. - 2017. - 69, № 7. - pp. 925-932
We establish asymptotic expansions for the values of approximation of functions from the H¨older class by biharmonic Poisson integrals in the uniform and integral metrics.
Approximation of (ψ, β)-differentiable functions of low smoothness by biharmonic Poisson integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2011. - 63, № 12. - pp. 1602-1622
We solve the Kolmogorov – Nikol’skii problem for biharmonic Poisson integrals on the classes of (ψ, β)- differentiable periodic functions of low smoothness in the uniform metric.
Approximation of functions from the classes $C^{\psi}_{\beta, \infty}$ by biharmonic Poisson integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 939-959
Asymptotic equalities are obtained for upper bounds of deviations of biharmonic Poisson integrals on the classes of $(\psi, \beta)$-differentiable periodic functions in the uniform metric.
Approximation of conjugate differentiable functions by biharmonic Poisson integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2009. - 61, № 3. - pp. 333-345
We determine the exact values of upper bounds of approximations by biharmonic Poisson integrals on classes of conjugate differentiable functions in uniform and integral metrics.
Approximation of conjugate differentiable functions by their Abel–Poisson integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 73-82
We obtain the exact values of upper bounds of approximations of classes of periodic conjugate differentiable functions by their Abel–Poisson integrals in uniform and integral metrics.
Approximation of Differentiable Periodic Functions by Their Biharmonic Poisson Integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1213-1219
We determine the exact values and asymptotic decompositions of upper bounds of approximations by biharmonic Poisson integrals on classes of periodic differentiable functions.
Complete Asymptotics of the Deviation of a Class of Differentiable Functions from the Set of Their Harmonic Poisson Integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2002. - 54, № 1. - pp. 43-52
On a class of differentiable functions W r and the class \(\overline W ^r \) of functions conjugate to them, we obtain a complete asymptotic expansion of the upper bounds \(\mathcal{E}(\mathfrak{N},A\rho )_C \) of deviations of the harmonic Poisson integrals of the functions considered.
On the Approximation of Functions of the Hölder Class by Triharmonic Poisson Integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2001. - 53, № 6. - pp. 855-859
We determine the exact value of the upper bound for the deviation of the triharmonic Poisson integral from functions of the Hölder class.
On the Approximation of Functions of the Hölder Class by Biharmonic Poisson Integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 971-974
We determine the exact value of the upper bound of the deviation of biharmonic Poisson integrals from functions of the Hölder class.