M. Ye. Tkachenko

• Docent at Oles Honchar Dnipro National University

Володимир Олександрович Кофанов (до 75-річчя від дня народження)

We consider the best $L_1$-approximation with interpolatory constraints for continuous mapping of a metric compact set $Q$ into a Banach space $X$. The unicity set’s criterion is obtained. This result generalizes the result for real functions that was proved by A. Pinkus and H. Strauss.

Владислав Федорович Бабенко (до 75-річчя від дня народження)

The criterion of the best non-symmetric approximant for $n$-variable functions in the space $L_{1, p_2,...,p_n}$ $(1<p_i<+\infty , i=2,3,...,n)$ with $(\alpha ,\beta )$-norm$$\|f\|_{1,p_2,...,p_n;\alpha,\beta}=\left[\int\limits_{a_n}^{b_n}\cdots\left[\int\limits_{a_2}^{b_2}\left[\int\limits_{a_1}^{b_1} |f(x)|_{\alpha,\beta} dx_1\right]^{p_2} dx_2\r...

The article considers the questions of the uniqueness of the best non-symmetric $L_1$-approximations of continuous functions with values in $\mathbb{R}^m_p, p\in (1;+\infty )$ by elements of the two-dimensional subspace $H_2= \mathrm{span} \{1, g_{a,b}\}$, where $$ g_{a,b}(x)=\left\{ \begin{matrix} -b\cdot (x-1)^2, & x\in [0;1), & \\ 0, & x\in [1...

The article is devoted to the talented mathematician, candidate of physical and mathematical sciences Boitsun Lilia Georgiivna. The article describes her life and career, scientific activity.

We obtain the conditions of unicity of the best $L_1$-approximant for vector-valued functions, continuous on metric compact, by subspace of constant mappings.

The conditions of uniqueness of the best non-symmetric $L_1$-approximant for continuous, on metric compact, vector-valued functions by the subspace of the constants are obtained.

The conditions of the unicity of the best nonsymmetric $L_1$-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

The questions of the uniqueness of the best non-symmetric $L_1$-approximant with weight in the finite dimensional subspace and the connection of such tasks with $A_{\alpha ,\beta }$-subspaces were considered in this article. This result generalizes the known result of Kroo on the case of non-symmetric approximation.

The questions of the characterization of the best approximant in spaces of multivariable functions with mixed integral metric with weight were considered in this article. The general form of a bounded linear functional and the criterion of the best approximant in these spaces are obtained.

In 2019 the Department of Mathematical Analysis and Theory of Functions celebrates its 100th anniversary. The history of its creation and development is given in the article in terms of the anniversary. Great attention is given to the famous mathematicians who have made a considerable contribution to the direction of the department’s scientific sch...

We investigate the problem of uniqueness of the best non-symmetrical $L_1$-approximant with a weight for continuous functions on metric compact set $Q$ with values in strictly convex partially ordered KB-space $X$ by subspaces of space $C(Q, X)$ of continuous functions on $Q$ with values in $X$. We obtain the characterization of subspaces of unique...

The article describes the main milestones of the life of the professor of mathematics G. О. Gruzintsev and some aspects of his research work in mathematics and in the theory of science. The list of the main works of G. О. Gruzintsev is given.

The questions of the characterization of the best approximant for the multivariable functions in the space with mixed integral metric were considered in this article. The criterion of the best approximant in space $$$L_{p_1,...,p_{i-1},1,p_{i+1},...,p_n}$$$ is obtained.

The questions of the characterization of the best non-symmetric $L_p$ and $L_1$-approximant for the functions with values in KB-space with a weight were considered. The criterions of the best non-symmetric approximant for the specified functions in metrics of the spaces $L_p$ and $L_1$ with a weight is obtained.

The questions of the characterization of the best approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterions of the best approximant in spaces $L_{1,p_2,...,p_n}$ and $L_{p_1,...,p_{n-1},1}$ is obtained.

The questions of the characterization of the best nonsymmetric approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterion of best nonsymmetric approximant in these spaces is obtained.

The questions of the characterization of the best approximant in spaces with mixed integral metric with weight were considered in this article. The general form of a bounded linear functional and the criterion of best approximant in these spaces are obtained.

The necessary and sufficient conditions of the unicity of the best $(\overline{\alpha},\overline{\beta})$-approximant with coefficient constraints for the continuous vector-valued functions on a metric compact are obtained.

The necessary and sufficient conditions of the unicity of the best $(\overline{\alpha};\overline{\beta})$-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

The necessary and sufficient conditions of the unicity of the best nonsymmetric approximant with coefficient constraints for the continuous vector-valued functions on a metric compact are obtained.

We consider the problem of characterization of subspaces of uniqueness of an element of the best nonsymmetric L We consider the problem of characterization of subspaces of uniqueness of an element of the best nonsymmetric L 1-approximation of functions that are continuous on a metric compact set of functions with values in a KB-space. We find class...

We study the problem of uniqueness of an element of the best L 1-approximation for continuous functions with values in a Banach space. We prove two theorems that characterize the uniqueness subspaces in terms of certain sets of test functions.

Two classes of test function h in C(Q) which characterize the subspaces of uniqueness for the best non-symmetric L1-approximation of continuous functions on a metrically convex metric compact Q are described.