Abdullayev, F. G. Serdyuk, A. S. Shidlich, A. L.
Published in
Ukrainian Mathematical Journal
We obtain exact Jackson-type inequalities in terms of the best approximations and averaged values of the generalized moduli of smoothness in the spaces Sp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsid...
Atlasiuk, O. M. Mikhailets, V. A.
Published in
Ukrainian Mathematical Journal
For systems of ordinary differential equations on a compact interval, we study the character of solvability of the most general linear boundary-value problems in Sobolev spaces. We find the indices of these problems and obtain a criterion of their well-posedness.
Vakarchuk, S. B.
Published in
Ukrainian Mathematical Journal
We consider the generalized characteristics of smoothness of the functions ωw(f, t) and Λw(f, t), t > 0, in the space L2(ℝ) and on the classes L2α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}...
Guseinov, I. M. Khanmamedov, Ag. Kh.
Published in
Ukrainian Mathematical Journal
We consider a one-dimensional Schrödinger equation on the entire axis whose potential rapidly decreases on the left-hand side and infinitely increases on the right-hand side. By the method of transformation operators, we study the inverse scattering problem. We establish conditions for the scattering data under which the inverse problem is solvable...
Gryshchuk, S. V.
Published in
Ukrainian Mathematical Journal
For an algebra B0≔c1e+c2ω:ck∈ℂk=12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbbm{B}}_0:= \left\{{c}_1e+{c}_2\omega :{c}_k\in \mathbb{C},k=1,2\right\} $$\end...
Bandura, A. I. Skaskiv, O. B.
Published in
Ukrainian Mathematical Journal
We consider the following compositions of entire functionsFz=fΦzandHzw=GΦ1zΦ1w,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ F(z)=f\left(\varPhi (z)\right)\kern0.5em...
Tiryaki, A.
Published in
Ukrainian Mathematical Journal
We establish Caccioppoli-type estimates for a class of nonlinear differential equations with the help of a differential identity that generalizes the well-known multidimensional Picone formula. In special cases, these estimates give the Finsler p-Laplacian, the p-Laplacian, and the pseudo-p-Laplacian.
Vakarchuk, S. B.
Published in
Ukrainian Mathematical Journal
In the second part of the paper, we establish the exact Jackson-type inequalities for the characteristic of smoothness Λw on the classes of functions L2αι\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsid...
Gryshchuk, S. V.
Published in
Ukrainian Mathematical Journal
The author’s name should read S. V. Gryshchuk.
Markitan, V. P. Prats’ovytyi, M. V. Savchenko, I. O.
Published in
Ukrainian Mathematical Journal
We consider a family of convergent positive normed series with real terms defined by the conditions where (an) is a nondecreasing sequence of real numbers. The structural properties of these series are investigated. For a special case, namely, an=2n−1,cn=n+1r˜n,n∈ℕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{a...
