One-sided estimates for the existence of null points of holomorphic mappings in Banach spaces

Journal of Mathematical Analysis and Applications

Volumn 203, Issue 1, 1996, Pages 38-54

  Aizenberg, L ^a   Reich, S ^b   Shoikhet, D ^c  

^a BAR ILAN UNIVERSITY   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c International College of Technology   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030268542     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0366     Document Type: Article

References (31)

1. [AL] L. Aizenberg, "Carleman's Formulas in Complex Analysis," Kluwer Academic, Dordrecht, 1993.
2. [AH] H. Amann, Existence theorems for equations of Hammerstein type, Appl. Anal. 1 (1972), 385-397.
3. [AJ] J. Arazy, An application of infinite dimensional holomorphy to the geometry of Banach spaces, in "Lecture Notes in Math.," Vol. 1267, pp. 122-150, Springer-Verlag, Berlin, 1987.
4. [BH] H. Brezis, Équations et inéquations non-linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier 18 (1968), 115-175.
5. [BF1] F. E. Browder, Nonlinear elliptic boundary value problems, Bull. Amer. Math. Soc. 69 (1963), 862-874.
6. [BF2] F. E. Browder, Nonlinear functional analysis and nonlinear integral equations of Hammerstein and Urysohn type, in "Contributions to Nonlinear Functional Analysis," pp. 425-500, Academic Press, New York, 1971.
7. [E-H] C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, in "Proc. Sympos. Pure Math.," Vol. 16, pp. 61-65, Amer. Math. Soc., Providence, RI, 1970.
8. [FK] K. Fan, A minimax inequality and applications, in "Inequalities III," pp. 103-113, Academic Press, New York, 1972.
9. [F-V] T. Franzoni and E. Vesentini, "Holomorphic Maps and Invariant Distances," North-Holland, Amsterdam, 1980.
10. [G-R] K. Goebel and S. Reich, "Uniform Convexity, Hyperbolic Geometry and Nonex-pansive Mappings," Dekker, New York, Basel, 1984.
11. [H-M] U. Helmke and J. B. Moore, "Optimization and Dynamical Systems," Springer-Verlag, London, 1994.
12. [HM] M. Hervé, "Analyticity in Infinite Dimensional Spaces," de Gruyter, Berlin, 1989.
13. [I-S] J. M. Isidro and L. L. Stacho, "Holomorphic Automorphism Groups in Banach Spaces: An Elementary Introduction," North-Holland, Amsterdam, 1984.
14. [K-R-S] V. Khatskevich, S. Reich, and D. Shoikhet, Fixed point theorems for holomorphic mappings and operator theory in indefinite metric spaces, Integral Equations Operator Theory, 22 (1995), 305-316.
15. [Kh-Sh] V. Khatskevich and D. Shoikhet, "Differentiable Operators and Nonlinear Equations," Birkhäuser, Basel, 1994.
16. [KM] M. A. Krasnoselskii, On a boundary problem, Izv. Akad. Nauk SSSR Ser. Mat. 20 (1956), 241-252.
17. [K-Z] M. Krasnoselskii and P. Zabreiko, "Geometrical Methods of Nonlinear Analysis," Springer-Verlag, Berlin, 1984.
18. [KS] S. Krein, "Functional Analysis," Nauka, Moscow, 1972.
19. [K-S] T. Kuczumow and A. Stachura, Fixed points of holomorphic mappings in Cartesian products of n unit Hilbert balls, Canad. Math. Bull. 29 (1986), 281-286.
20. [MA] A. J. Markushevich, "Theory of Analytic Functions," Nauka, Moscow, 1986.
21. [M-V] P. Mazet and J.-P. Vigué, Points fixes d'une application holomorphe d'un domain borné dans lui-même, Acta Math. 166 (1991), 1-26.
22. [RS1] S. Reich, Minimal displacement of points under weakly inward pseudo-lipschitzian mappings, Atti Accad. Naz. Linzei Rend. Cl. Sci. Fis. Mat. Natur. 59 (1975), 40-44.
23. [RS2] S. Reich, Approximate selections, best approximations, fixed points, and invariant sets, J. Math. Anal. Appl. 62 (1978), 104-113.
24. [R-S] S. Reich and D. Shoikhet, Generation theory for semigroups of holomorphic mappings in Banach spaces, Technion Preprint Series, No. MT-1007, 1995, Abstr. Appl. Anal. 1 (1996), 1-44.
25. n", Springer-Verlag, Berlin, 1980.
26. [SM] M. Shinbrot, A fixed point theorem and some applications, Arch. Rational Mech. Anal. 17 (1964), 255-271.
27. [TV] V. A. Trenogin, "Functional Analysis," Nauka, Moscow, 1980.
28. [UH] H. Upmeier, "Jordan Algebras in Analysis, Operator Theory and Quantum Mechanics," CBMS-NSF Regional Conf. Ser. in Math., SIAM, Philadelphia, 1987.
29. [VM] M. M. Vainberg, "Variational Methods for the Study of Nonlinear Operators," Holden-Day, San Francisco, 1964.
30. [V-T] M. M. Vainberg and V. A. Trenogin, "Theory of Bifurcation of Solutions of Nonlinear Equations," Nauka, Moscow, 1969.
31. [YK] K. Yosida, "Functional Analysis," Springer-Verlag, Berlin, 1968.