V. Babenko

activity

20132024

most citedOn Landau -- Kolmogorov type inequalities for charges and their applications

4 citations · 18 across the 17 of their papers we have counts for

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Showing 2013Show all

4 papers · 1 filter

math.NA2013★ 2 cited

Exact asymptotics of the optimal Lp-error of asymmetric linear spline approximation

Vladyslav Babenko, Yuliya Babenko, Nataliya Parfinovych +1

In this paper we study the best asymmetric (sometimes also called penalized or sign-sensitive) approximation in the metrics of the space $L_{p}$ , $1 ⩽ p ⩽ \infty$ , of fu…

math.FA2013

Comparison theorems and some of their applications

Vladyslav Babenko, Oleg Kovalenko

Analogues of Kolmogorov comparison theorems and some of their applications were established.

math.FA2013★ 1 cited

On dependence between the norm of a function and norms of its derivatives of orders k, r - 2 and r, 0 < k < r - 2

Vladyslav Babenko, Oleg Kovalenko

Necessary and sufficient conditions on the system of positive numbers $M_{k_{1}}, M_{k_{2}}, M_{k_{3}}, M_{k_{4}}$ , $0 = k_{1} < k_{2} < k_{3} = r - 2$ , $k_{4} = r$ , which guarantee the existence of a fun…

math.FA2013

Kolmogorov's Problem on the Class of Multiply Monotone Functions

Vladyslav Babenko, Yuliya Babenko, Oleg Kovalenko

In this paper we give necessary and sufficient conditions for the system of positive numbers $M_{k_{1}}, M_{k_{2}}, ..., M_{k_{d}},$ $0 \leq k_{1} < ... < k_{d} \leq r$ , to guarantee the ex…