# FIXED POINT THEORY FOR VARIOUS CLASSES OF PERMISSIBLE MAPS VIA INDEX THEORY

Agarwal, Ravi P.;O'Regan, Donal

• Published : 2009.04.30
• 54 6

#### Abstract

In this paper we use degree and index theory to present new applicable fixed point theory for permissible maps.

#### Keywords

fixed point theory;projective limits

#### References

1. R. P. Agarwal, M. Frigon, and D. O'Regan, A survey of recent fixed point theory in Frechet spaces, Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday, Vol 1, 75–88, Kluwer Acad. Publ., Dordrecht, 2003
2. R. P. Agarwal and D. O'Regan, Countably P–concentrative pairs and the coincidence index, Applied Math. Letters 12 (2002), 439–444 https://doi.org/10.1016/S0893-9659(01)00156-2
3. R. P. Agarwal and D. O'Regan, A topological degree for pairs, Fixed Point Theory and Applications Vol 4 (edited by Y. J. Cho, J. K. Kim, and S. M. Kang), Nova Science Publishers, New York, 2003, 11–17
4. R. P. Agarwal and D. O'Regan, Multivalued nonlinear equations on the half line: a fixed point approach, Korean Jour. Computational and Applied Math. 9 (2002), 509–524
5. J. Andres, G. Gabor, and L. Gorniewicz, Boundary value problems on infinite intervals, Trans. Amer. Math. Soc. 351 (1999), 4861–4903 https://doi.org/10.1090/S0002-9947-99-02297-7
6. Z. Dzedzej, Fixed point index for a class of nonacyclic multivalued maps, Diss. Math. 253 (1985), 1–58
7. P. M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems and fixed point index for multivalued mappings in cones, J. London Math. Soc. 12 (1975), 75–82 https://doi.org/10.1112/jlms/s2-12.1.75
8. L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Publishers, Dordrecht, 1999
9. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1964
10. Z. Kucharski, A coincidence index, Bull. Acad. Polon. Sci. 24 (1976), 245–252
11. R. Ma, D. O'Regan, and R. Precup, Fixed point theory for admissible pairs and maps in Fr´echet spaces via degee theory, Fixed Point Theory 8 (2007), 273–283
12. D. O'Regan, An essential map approach for multimaps defined on closed subsets of Frechet spaces, Applicable Analysis 85 (2006), 503–513 https://doi.org/10.1080/00036810500474861
13. D. O'Regan, Fixed point theory in Frechet spaces for permissible Urysohn type maps, to appear
14. D. O'Regan, Y. J. Cho, and Y. Q. Chen, Topological Degree Theory and Applications, Chapman and Hall/CRC, Boca Raton, 2006
15. R. P. Agarwal and D. O'Regan, An index theory for countably P-concentrative J maps, Applied Math. Letters 16 (2003), 1265–1271 https://doi.org/10.1016/S0893-9659(03)90127-3
16. R. Bader and W. Kryszewski, Fixed point index for compositions of set valued maps with proximally $\infty$-connected values on arbitrary ANR's, Set Valued Analysis 2 (1994), 459–480 https://doi.org/10.1007/BF01026835
17. L. Gorniewicz, A. Granas, and W. Kryszewski, On the homotopy method in the fixed point index theory of multi–valued mappings of compact absolute neighborhood retracts, Jour. Math. Anal. Appl. 161 (1991), 457–473 https://doi.org/10.1016/0022-247X(91)90345-Z
18. M. Vath, Fixed point theorems and fixed point index for countably condensing maps, Topological Methods in Nonlinear Analysis, 13 (1999), 341–363