Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T10:38:13.601Z Has data issue: false hasContentIssue false

Zeros of Nonlinear Monotone Operators in Hilbert Space*

Published online by Cambridge University Press:  20 November 2018

R. Schöneberg*
Affiliation:
Lehrstuhl C Für Math., Rwth Aachen, 5100 Aachen Fed. Rep. of Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Around 1960, the Russian mathematician Kachurovski [1] introduced the notion of monotone operators in Hilbert spaces: Let E be a Hilbert space and X ⊂ E. An operator T:X→E is said to be monotone, iff

.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Kachurovski, R. I., On monotone operators and convex junctionals, Uspehi Mat. Nauk 15, 213-215 (1960).Google Scholar
2. Crandall, M. and Pazy, A., Semigroups of nonlinear contractions and dissipative sets, J. Functional Analysis 3, 376-418 (1969).Google Scholar
3. Browder, F. E., Remarks on non-linear functional equations III, Illinois J. Math. 9, 617-622 (1965).Google Scholar
4. Schoenberg, I. J., On a theorem of Kirszbraun and Valentine, Amer. Math. Monthly 60, 620-622 (1953).Google Scholar
5. Browder, F. E., Fixed point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 53, 1272-1276 (1965).Google Scholar
6. Reinermann, J. and Sch, R.ôneberg, Some results in fixed point theory for nonexpansive and pseudo- contractive mappings in Hilbert space, Proceedings of a Seminar on Fixed Point Theory and its Applications, Dalhousie University, Halifax, N.S., June 9-12 (1975), Academic Press.Google Scholar
7. Kirk, W. A. and Sch, R.ôneberg, Some results on pseudo-contractive mappings, Pacific J. Math., 71, 89-100 (1977).Google Scholar
8. Reinermann, J. and Stallbohm, V., Fixed point theorems for compact and nonexpansive mappings on starshaped domains, Math. Balkanica 4. 95, 511-516 (1974).Google Scholar
9. CI. Krauthausen, Miiller, G., Reinermann, J. and Sch, R.ôneberg, New fixed point theorems for compact and nonexpansive mappings and applications to Hammerstein equations, Sonderforschungsbereich 72, Universitât Bonn, preprint no. 92, 108 p., 1976.Google Scholar
10. Browder, F. E. and Figueiredo, D. G. de, J-monotone nonlinear operators in Banach spaces, Indag. Math. 28, 412-420 (1966).Google Scholar