Abstract
Some new fixed point theorems for approximable maps are obtained in this paper. Homotopy results, via essential maps, are also presented for approximable maps.
Authors
Ravi P. Agarwal
Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida 32901, USA
Donal O’Regan
Department of Mathematics, National University of Ireland, Galway, IRELAND
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Fixed points; homotopy; approximable; Leray-Schauder alternative; topological vector space
Paper coordinates
R.P. Agarwal, D. O’Regan, R. Precup, Fixed point theory and generalized Leray-Schauder alternatives for approximable maps in topological vector spaces, Topol. Methods Nonlinear Anal. 22, no. 1 (2003), 193-202, https://doi.org/10.12775/TMNA.2003.036
About this paper
Journal
Topological Methods Nonlinear Analysis
Publisher Name
Journal of the Juliusz Schauder Center
Print ISSN
Online ISSN
12303429
MR 2037275, Zbl pre02096725
google scholar link
[1] R. P. Agarwal and D. O’Regan, Homotopy and Leray–Schauder principles for multimaps, Nonlinear Anal. Forum 7 (2002 pages 103–111).
[2] C. D. Aliprantis and K. C. Border, Infinite dimensional analysis, Springer–Verlag Berlin, 1994.
[3] H. Ben-El-Mechaiekh, S. Chebbi and M. Florenzano, A Leray–Schauder type theorem for approximable maps: a simple proof, Proc. Amer. Math. Soc. 126 (1998 pages 2345–2349).
[4] H. Ben-El-Mechaiekh and P. Deguire, Approachability and fixed points for nonconvex set valued maps, J. Math. Anal. Appl. 170 (1992 pages 477–500).
[5] L. Gorniewicz, Topological Fixed Point Theory of Multivalued Maps, Kluwer Acad. Publishers, Dordrecht, 1999.
[6] I. Kim, K. Kim and S. Park, Leray–Schauder alternatives for approximable maps in topological vector spaces, Math. Comput. Modelling 35 (2002 pages 385–391).
[7] D. O’Regan, Fixed point theory for closed multifunctions, Arch. Math. (Brno) 34 (1998), 191–197.
[8] S. Park, A unified fixed point theory of multimaps on topological vector spaces, J. Korean Math. Soc. 35 (1998 pages 803–829).
[9]___The Leray–Schauder principles for condensing approximable and other multimaps, Nonlinear Anal. Forum 4 (1999 pages 157–173).
[10] F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.