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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
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