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Fixed point theorems for compositions of set-valued maps with single-valued maps. (English) Zbl 1012.47043
Summary: Some fixed point theorems are presented for a class of set-valued maps which seems to be interesting in view of applications in the theory of differential equations and inclusions. Our approach is based upon the topological fixed point theory initiated in [L. Górniewicz, A. Granas and W. Kryszewshi, J. Math. Anal. Appl. 161, 457-473 (1991; Zbl 0757.54019)] and developed in [R. Bader, Ph. D. Dissertation, Munich (1995; Zbl 0865.47049)].

##### MSC:
 47H11 Degree theory for nonlinear operators 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems 47H04 Set-valued operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 54C60 Set-valued maps in general topology