Abstract
We study the existence problems of fixed points and the topological structure of fixed point sets for nonexpansive set-valued maps in Banach space. We establish some porosity results on the existence of fixed points and the topological structure of fixed point sets for nonexpansive set-valued maps with values in an admissible family. The results obtained in the present paper cover and improve the corresponding ones due to De Blasi and Myjak (C. R. Acad. Sci. Paris Sér. I Math. 308:51–54, 1989) and De Blasi et al. (Set-Valued Anal. 17:97–112, 2009).
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Peng, L., Li, C. Porosity and Fixed Points of Nonexpansive Set-Valued Maps. Set-Valued Var. Anal 22, 333–348 (2014). https://doi.org/10.1007/s11228-013-0265-0
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DOI: https://doi.org/10.1007/s11228-013-0265-0