A fixed point index for generalized inward mappings of condensing type
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- by Kunquan Lan and Jeffrey Webb PDF
- Trans. Amer. Math. Soc. 349 (1997), 2175-2186 Request permission
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.References
- M. V. Reĭn, A general method of lowering the order of a Hamiltonian system with a known integral, Dokl. Akad. Nauk SSSR 158 (1964), 294–297 (Russian). MR 0170509
- Klaus Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985. MR 787404, DOI 10.1007/978-3-662-00547-7
- Klaus Deimling, Positive fixed points of weakly inward maps, Nonlinear Anal. 12 (1988), no. 3, 223–226. MR 928556, DOI 10.1016/0362-546X(88)90108-3
- K. Deimling, Fixed points of weakly inward multis, Nonlinear Anal., 10 (1986), 1261–1262.
- Klaus Deimling and Shou Chuan Hu, Fixed points of weakly inward maps in conical shells, Nonlinear Anal. 12 (1988), no. 3, 227–230. MR 928557, DOI 10.1016/0362-546X(88)90109-5
- P. M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems and the fixed point index for multivalued mappings in cones, J. London Math. Soc. (2) 12 (1975/76), no. 1, 75–85. MR 405180, DOI 10.1112/jlms/s2-12.1.75
- P. M. Fitzpatrick and W. V. Petryshyn, Positive eigenvalues for nonlinear multivalued noncompact operators with applications to differential operators, J. Differential Equations 22 (1976), no. 2, 428–441. MR 435958, DOI 10.1016/0022-0396(76)90038-3
- Shou Chuan Hu and Yong Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl. 172 (1993), no. 1, 266–273. MR 1199511, DOI 10.1006/jmaa.1993.1023
- K. Q. Lan, Nonzero fixed point theorems for weakly inward $\alpha$-condensing maps, J. Sichuan Normal University, 1 (1989), 16–18.
- Roger D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. (4) 89 (1971), 217–258. MR 312341, DOI 10.1007/BF02414948
- 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), no. 3, 503–512. MR 972134, DOI 10.1112/jlms/s2-38.3.503
- W. V. Petryshyn, Multiple positive fixed points of multivalued condensing mappings with some applications, J. Math. Anal. Appl. 124 (1987), no. 1, 237–253. MR 883525, DOI 10.1016/0022-247X(87)90037-0
- Simeon Reich, Fixed point theorems for set-valued mappings, J. Math. Anal. Appl. 69 (1979), no. 2, 353–358. MR 538223, DOI 10.1016/0022-247X(79)90148-3
- B. N. Sadovskiĭ, Limit-compact and condensing operators, Uspehi Mat. Nauk 27 (1972), no. 1(163), 81–146 (Russian). MR 0428132
- Yong Sun and Jing Xian Sun, Multiple positive fixed points of weakly inward mappings, J. Math. Anal. Appl. 148 (1990), no. 2, 431–439. MR 1052354, DOI 10.1016/0022-247X(90)90011-4
- T. E. Williamson Jr., The Leray-Schauder condition is necessary for the existence of solutions, Fixed point theory (Sherbrooke, Que., 1980) Lecture Notes in Math., vol. 886, Springer, Berlin-New York, 1981, pp. 447–454. MR 643022
Additional Information
- Kunquan Lan
- Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK
- MR Author ID: 256493
- 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
- Received by editor(s): February 13, 1995
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 2175-2186
- MSC (1991): Primary 47H11, 47H09; Secondary 54H25
- DOI: https://doi.org/10.1090/S0002-9947-97-01939-9
- MathSciNet review: 1422903