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FIXED POINTS, EIGENVALUES AND SURJECTIVITY
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 Title & Authors
FIXED POINTS, EIGENVALUES AND SURJECTIVITY
Kim, In-Sook;
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 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;
 Language
English
 Cited by
1.
Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets, Central European Journal of Mathematics, 2013, 11, 1, 85  crossref(new windwow)
 References
1.
J. M. Ayerbe Toledano, T. Dominguez Benavides, and G. Lopez Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhauser, Basel, 1997

2.
K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985

3.
S. Hahn, Homoomorphieaussagen fur k-verdichtende Vektorfelder, Comment. Math. Univ. Carolin. 21 (1980), no. 3, 563-572

4.
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 crossref(new window)

5.
G. Isac and S. Z. Nemeth, Fixed points and positive eigenvalues for nonlinear operators, J. Math. Anal. Appl. 314 (2006), no. 2, 500-512 crossref(new window)

6.
G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29-43 crossref(new window)

7.
H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), no. 5, 985-999 crossref(new window)

8.
R. D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. (4) 89 (1971), 217-258 crossref(new window)

9.
W. V. Petryshyn, Remarks on condensing and k-set-contractive mappings, J. Math. Anal. Appl. 39 (1972), 717-741 crossref(new window)

10.
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 crossref(new window)

11.
M. Vath, Fixed point theorems and fixed point index for countably condensing maps, Topol. Methods Nonlinear Anal. 13 (1999), no. 2, 341-363

12.
A. Vignoli, On quasibounded mappings and nonlinear functional equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 50 (1971), 114-117

13.
E. Zeidler, Nonlinear Functional Analysis and its Applications. I., Springer-Verlag, New York, 1986