The Bojanov – Naidenov problem for functions with nonsymmetric restrictions on the highest derivative

  • V. A. Kofanov

Abstract

For given r\bfN,p,α,β,μ>0, we solve the extreme problems baxq±(t)dtsup,qp, in the set of pairs (x,I) of functions xLr and intervals I=[a,b]R satisfying the inequalities βx(r)(t)α for almost all tR , the conditions L(x±)pL((φα,βλ,r))p, and the corresponding condition μ(supp[a,b]x+)μ or μ(supp[a,b]x)μ, where L(x)p:=sup{xLp[a,b]:a,bR,|x(t)|>0,t(a,b)}, supp[a,b]x±:={t[a,b]:x±(t)>0},φα,βλ,r is the nonsymmetric (2π/λ)-periodic Euler spline of order r. As a consequence, we solve the same problems for the intermediate derivatives x(k)±,k=1,...,r1, with q1.
Published
25.03.2019
How to Cite
Kofanov, V. A. “The Bojanov – Naidenov Problem for Functions With Nonsymmetric restrictions on the Highest Derivative”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 3, Mar. 2019, pp. 368-81, https://umj.imath.kiev.ua/index.php/umj/article/view/1445.
Section
Research articles