The Bojanov-Naidenov problem for the functions with non-symmetric restrictions on the oldest derivative

  • Володимир Олександрович Кофанов Дніпровський національний університет імені Олеся Гончара

Abstract

For given r\NN, p,α,β,μ>0, we solve the
extremal problems
baxq±(t)dtsup,qp,
on the set of pair (x,I) functions xLr and
intervals I=[a,b]\RR satisfying the inequalities βx(r)(t)α for almost everywhere t\RR and
the both of conditions L(x±)pL(φα,βλ,r)±)p, and such that μ(supp[a,b]x+)μ or μ(supp[a,b]x)μ, where
L(x)p:=sup{
{\rm supp}_{[a, b]} x_{\pm}:= \{t\in [a, b]: x_{\pm}(t) > 0\}
and \varphi_{\lambda,r}^{\alpha, \beta} is the nonsymmetric
(2\pi/\lambda)-periodic spline of Euler of order r. In
particular, we solve the same problems for the intermediate
derivatives x^{(k)}_{\pm}, k=1,...,r-1, with q \ge 1.

 

Published
29.01.2021
How to Cite
Кофанов, В. О. “The Bojanov-Naidenov Problem for the Functions With Non-Symmetric Restrictions on the Oldest Derivative”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 3, Jan. 2021, pp. 368-81, https://umj.imath.kiev.ua/index.php/umj/article/view/254.
Section
Research articles