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http://dx.doi.org/10.4134/JKMS.2008.45.1.151

FIXED POINTS, EIGENVALUES AND SURJECTIVITY  

Kim, In-Sook (Department of Mathematics Sungkyunkwan University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 151-161 More about this Journal
Abstract
We prove that a countably condensing operator defined on a closed wedge in a Banach space has a fixed point if it is strictly quasibounded, by using an index theory for such operators. From this, the existence of eigenvalues and surjectivity are deduced.
Keywords
fixed points; eigenvalues; surjectivity; countably condensing maps;
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1 K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985
2 G. Isac and S. Z. Nemeth, Scalar derivatives and scalar asymptotic derivatives. An Altman type fixed point theorem on convex cones and some applications, J. Math. Anal. Appl. 290 (2004), no. 2, 452-468   DOI   ScienceOn
3 G. Isac and S. Z. Nemeth, Fixed points and positive eigenvalues for nonlinear operators, J. Math. Anal. Appl. 314 (2006), no. 2, 500-512   DOI   ScienceOn
4 G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29-43   DOI
5 H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), no. 5, 985-999   DOI   ScienceOn
6 R. D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. (4) 89 (1971), 217-258   DOI
7 W. V. Petryshyn, Remarks on condensing and k-set-contractive mappings, J. Math. Anal. Appl. 39 (1972), 717-741   DOI
8 W. V. Petryshyn and P. M. Fitzpatrick, A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings, Trans. Amer. Math. Soc. 194 (1974), 1-25   DOI   ScienceOn
9 M. Vath, Fixed point theorems and fixed point index for countably condensing maps, Topol. Methods Nonlinear Anal. 13 (1999), no. 2, 341-363   DOI
10 A. Vignoli, On quasibounded mappings and nonlinear functional equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 50 (1971), 114-117
11 E. Zeidler, Nonlinear Functional Analysis and its Applications. I., Springer-Verlag, New York, 1986
12 S. Hahn, Homoomorphieaussagen fur k-verdichtende Vektorfelder, Comment. Math. Univ. Carolin. 21 (1980), no. 3, 563-572
13 J. M. Ayerbe Toledano, T. Dominguez Benavides, and G. Lopez Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhauser, Basel, 1997