Transactions of the American Mathematical Society

Author(s): Kunquan Lan; Jeffrey Webb
Journal: Trans. Amer. Math. Soc. 349 (1997), 2175-2186.
MSC (1991): Primary 47H11, 47H09; Secondary 54H25
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Abstract: A fixed point index is defined for mappings defined on a cone $K$

which do not necessarily take their values in $K$

but satisfy a weak type of boundary condition called generalized inward. This class strictly includes the well-known weakly inward class. New results for existence of multiple fixed points are established.

1.: F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197-228. MR 30:747
2.: K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985. MR 86j:47001
3.: K. Deimling, Positive fixed points of weakly inward maps, Nonlinear Anal., 12 (1988), 223-226. MR 89b:47077
4.: K. Deimling, Fixed points of weakly inward multis, Nonlinear Anal., 10 (1986), 1261-1262.
5.: K. Deimling and Hu Shouchuan, Fixed points of weakly inward maps in conical shells, Nonlinear Anal., 12 (1988), 227-230. MR 89d:47121
6.: P. M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems and the fixed point index for multivalued maps in cones, J. London Math. Soc., (2), 12 (1975), 75-85. MR 53:8974
7.: P. M. Fitzpatrick and W. V. Petryshyn, Positive eigenvalues for nonlinear multivalued operators with applications to differential operators, J. Differential Equations, 22 (1976), 428-441. MR 55:8909
8.: S. Hu and Y. Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl., 172 (1993), 266-273. MR 94a:47102
9.: K. Q. Lan, Nonzero fixed point theorems for weakly inward $\alpha$ -condensing maps, J. Sichuan Normal University, 1 (1989), 16-18.
10.: R. D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. 84 (1971), 217-258. MR 47:903
11.: W. V. Petryshyn, Existence of fixed points of positive k-set-contractive maps as consequences of suitable boundary conditions, J. London Math. Soc., (2) 38 (1988), 503-512. MR 90b:47108
12.: W. V. Petryshyn, Multiple positive fixed points of multivalued condensing mappings with some applications, J. Math. Anal. Appl., 124 (1987), 237-253. MR 88e:47103
13.: S. Reich, Fixed point theorems for set-valued mappings, J. Math. Anal. Appl., 69 (1979), 353-358. MR 80k:47068
14.: B. N. Sadovsky, Limit compact and condensing operators, Russian Math. Surveys, 27 (1972), no. 1, 85-155. MR 55:1161
15.: Y. Sun and J. Sun, Multiple positive fixed points of weakly inward mappings, J. Math. Anal. Appl., 148 (1990), 431-439. MR 91f:47084
16.: T. E. Williamson Jr, The Leray-Schauder condition is necessary for the existence of solutions, Fixed Point Theory, Proc., Sherbrooke, Quebec 1980, Editors, E. Fadell and G. Fournier, Lecture Notes in Mathematics 886, Springer-Verlag, 1981, 447-454. MR 83j:47042

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 47H11, 47H09, 54H25

Kunquan Lan
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK
Email: kl@maths.gla.ac.uk

Jeffrey Webb
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK
Email: jrlw@maths.gla.ac.uk

DOI: 10.1090/S0002-9947-97-01939-9
PII: S 0002-9947(97)01939-9
Keywords: Generalized inward, weakly inward, condensing maps
Received by editor(s): February 13, 1995
Copyright of article: Copyright 1997, American Mathematical Society

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