Article
Keywords:
Nemitskii operator; Hölder spaces
Summary:
The paper is concerned with the Nemitskii operator in Hölder spaces. Namely conditions are given to ensure acting, continuity, Lipschitz and differentiability properties.
References:
[1] Appell J.:
The superposition operator in function spaces - A survey. Expo. Math. 6 (1975), 209-270.
MR 0949784
[2] Appell J., Zabreiko P.:
Nonlinear superposition operators. Cambridge Tracts in Mathematics 95, Cambridge University Press, 1990.
MR 1066204
[3] Bondarenko V.A., Zabreiko P.: The superposition operator in Hölder function spaces. Soviet Math. Dokl. 16 (1975), 739-743.
[4] Drábek P.:
Continuity of Němickij's operator in Hölder spaces. Comment. Math. Univ. Carolinae 16 (1975), 37-57.
MR 0380547
[5] Goebel M.:
On Fréchet differentiability of Nemitskij operators acting in Hölder spaces. Glasgow Math. J. 33 (1991).
MR 1089947
[6] Goebel M.:
Continuity and Fréchet differentiability of Nemitskij operators in Hölder spaces. Monatshefte für Mathematik 113 (1992), 107-119.
MR 1154474
[7] Nugari R.:
Continuity and differentiability properties of the Nemitskij operator in Hölder spaces. Glasgow Math. J. 30 (1988), 59-65.
MR 0925559
[8] Valent T.:
Boundary value problems in finite elasticity. Springer Tracts in Natural Philosophy 31, Springer-Verlag, New York, 1988.
MR 0917733