an:04194540
Zbl 0724.47041
Goebel, Manfred
On Fr??chet-differentiability of Nemytskij operators acting in H??lder spaces
EN
Glasg. Math. J. 33, No. 1, 1-5 (1991).
00156339
1991
j
47H30 46E15 26A16
Nemytskij operator; H??lder space
The author considers the Nemytskij operator \(Fy(t)=f(y(t))\), generated by some continuous real function f, in the H??lder space \(H^{\nu}[a,b]\) \((0<\nu \leq 1)\). He proves that, if f is of class \(C^ 1\) [resp. \(C^ 2]\), the operator F is continuous [resp. continuously Fr??chet differentiable] on \(H^{\nu}[a,b]\). Related work is due, among others, to \textit{R. Nugari} [Glasgow J. Math. 30, 59-65 (1988; Zbl 0637.47035)] and \textit{T. Valent} [Springer Tracts Nat. Philos. 31 (1987; Zbl 0648.73019)]. A parallel study for the non-autonomous case \(f=f(t,y)\) will be published by the same author in Monatsh. Math. (to appear).
J.Appell (W??rzburg)
Zbl 0637.47035; Zbl 0648.73019