Open AccessBojanov-Naidenov problem for positive (negative) parts of differentiable functions on the real domain
Author(s) -
V.V. Kameneva,
В. А. Кофанов
Publication year - 2018
Publication title -
vìsnik dnìpropetrovsʹkogo unìversitetu. serìâ matematika
Language(s) - English
Resource type - Journals
eISSN - 2518-7996
pISSN - 2312-9557
DOI - 10.15421/241804
Subject(s) - differentiable function , measure (data warehouse) , domain (mathematical analysis) , combinatorics , mathematics , norm (philosophy) , function (biology) , physics , mathematical analysis , computer science , data mining , philosophy , epistemology , evolutionary biology , biology
We solve the extremal problem $$$\| x^{(k)}_{\pm} \|_{L_p[a,b]} \rightarrow \sup$$$, $$$k = 0, 1, ..., r-1$$$, over the set of pairs $$$(x, I)$$$ of functions $$$x\in W^r_{\infty} (\mathbb{R})$$$ and intervals $$$I = [a,b]$$$ with restrictions on the local norm of function $$$x$$$ and the measure of support $$$\mu \{ \mathrm{supp}_{[a,b]} x^{(k)}_{\pm} \}$$$.