Scalar derivatives and scalar asymptotic derivatives. An altman type fixed point theorem on convex cones and some applications

Journal of Mathematical Analysis and Applications

Volumn 290, Issue 2, 2004, Pages 452-468

  Isac, G ^a   Nemeth S Z ^b  

^a ROYAL MILITARY COLLEGE OF CANADA   (Canada)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10744231356     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.10.030     Document Type: Article

References (18)

1. R.R. Akhmerov, M.I. Kamenskii, A.S. Potapova, A.E. Rodkina, B.N. Sadovskii, Measure of Noncompactness and Condensing Operators, Birkhäuser, Basel, 1992.
2. M. Altman, A fixed point theorem in Hilbert spaces, Bull. Acad. Polon. Sci. 5 (1957) 19-22.
3. J. Banas, K. Goebel, Measure of Noncompactness in Banach Spaces, Dekker, New York, 1980.
4. M.P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992.
5. W. Feng, A new spectral theory for nonlinear operators and its applications, Abstr. Appl. Anal. 2 (1997) 163-183.
6. J.R. Giles, Classes of semi-inner-product spaces, Trans. Amer. Math. Soc. 129 (1967) 436-446.
7. P.J.H. Hedenmalm, Spectral properties of invariant subspaces in the Bergman space, J. Funct. Anal. 116 (1993) 441-448.
8. G. Isac, On an Altman type fixed point theorem on convex cones, Rocky Mountain J. Math. 25 (1995) 701-714.
9. G. Isac, The scalar asymptotic derivative and the fixed point theory on cones, Nonlinear Anal. Related Topics 2 (1999) 92-97.
10. G. Isac, S.Z. Németh, Scalar derivatives and scalar asymptotic derivatives. Properties and some applications, J. Math. Anal. Appl., in press.
11. G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961) 29-43.
12. S.Z. Németh, A scalar derivative for vector functions, Riv. Mat. Pura Appl. 10 (1992) 7-24.
13. S.Z. Németh, Scalar derivatives and spectral theory, Mathematica 35 (1993) 49-58.
14. R.D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. 84 (1971) 217-258.
15. S. Richter, Invariant subspaces in Banach spaces of analytic functions, Trans. Amer. Math. Soc. 304 (1987) 585-616
16. B.N. Sadovsky, Limit compact and condensing operators, Russian Math. Surveys 27 (1972) 85-155.
17. B.N. Shinbrot, A fixed point theorem and some applications, Arch. Rational Mech. Anal. 17 (1965) 255-271.
18. P.P. Zabreyko, A.I. Koshelev, M.A. Krasnoselskii, S.G. Mikhlin, L.S. Rakovshchik, V.Ya. Stetsenko, Integral Equations. A Reference Text, Noordhoff, 1975.