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On Fréchet-differentiability of Nemytskij operators acting in Hölder spaces

Published online by Cambridge University Press:  18 May 2009

Manfred Goebel
Manfred Goebel
Affiliation:
Martin-Luther-Universität, Sektion Mathematik, Universitätsplatz 6, G.D.R.-4020 Halle (Saale)
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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].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 1 , January 1991 , pp. 1 - 5
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Appell, J., The superposition operator in function spaces — a survey. Preprint 141 (Mathematisches Institut Universität Augsburg, 1987).Google Scholar
2.Appell, J., Zabrejko, P. P., Nonlinear superposition operators, Cambridge Tracts in Mathematics 95 (Cambridge University Press, 1989).Google Scholar
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.CrossRefGoogle Scholar
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.Drábek, P., Continuity of Nemytskij's operator in Hölder spaces, Comment. Math. Univ. Carotin. 16 (1975) 37–57.Google Scholar
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.Nugari, R., Continuity and differentiability properties of the Nemitskii operator in Hölder spaces, Glasgow Math. J. 30 (1988), 59–65.CrossRefGoogle Scholar
8.Pröβdorf, S., Einige Klassen singulärer Gleichungen (Akademie-Verlag, 1974).CrossRefGoogle Scholar