Geodesic
On Fréchet-differentiability of Nemytskij operators acting in Hölder spaces
Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 1-5

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In any field of nonlinear analysis Nemytskij operators, the superposition operators generated by appropriate functions, play a crucial part. Their analytic properties depend on the postulated properties of the defining function and on the function space in which they are considered. A rich source for related questions is the monograph by J. Appell and P. P. Zabrejko [2] and the survey paper by J. Appell [1]. 
Goebel, Manfred. On Fréchet-differentiability of Nemytskij operators acting in Hölder spaces. Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 1-5. doi: 10.1017/S0017089500007965
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[1] 1.Appell, J., The superposition operator in function spaces — a survey. Preprint 141 (Mathematisches Institut Universität Augsburg, 1987). Google Scholar

[2] 2.Appell, J., Zabrejko, P. P., Nonlinear superposition operators, Cambridge Tracts in Mathematics 95 (Cambridge University Press, 1989). Google Scholar

[3] 3.Appell, J., Pascale, E. De, Zabrejko, P. P., An application of B. N. Sadovskij's fixed point principle to nonlinear singular equations, Z. Anal. Anwendungen 6 (1987), 193–208. Google Scholar | DOI

[4] 4.Bondarenko, V. A., Zabrejko, P. P., The superposition operator in Hölder spaces (Russian), Dokl. Akad. Nauk SSR 222 (1975), 1265–1268. Google Scholar

[5] 5.Drábek, P., Continuity of Nemytskij's operator in Hölder spaces, Comment. Math. Univ. Carotin. 16 (1975) 37–57. Google Scholar

[6] 6.Goebel, M., Oestreich, D., Optimal control of a nonlinear singular integral equation arising in electrochemical machining, Z. Anal. Anwendungen, to appear. Google Scholar

[7] 7.Nugari, R., Continuity and differentiability properties of the Nemitskii operator in Hölder spaces, Glasgow Math. J. 30 (1988), 59–65. Google Scholar | DOI

[8] 8.Pröβdorf, S., Einige Klassen singulärer Gleichungen (Akademie-Verlag, 1974). Google Scholar | DOI

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