Über die Verallgemeinerten Fixpunktindizes von Iterierten Verdichtender Abbildungen

Abstract

The main result of this paper is the following theorem on the generalized fixed point index for locally condensing mappings: Let X be a subset of a Banach space such that there exists a locally finite covering {C_i|i∈I} of X by closed, convex subsets of X. If s=p^t with p prime and t∈N, M an open subset of X and g: D[g]→X with D[g]⊂X and M⊂D[g^S] such that g|M and g^S|M are locally condensing and the fixed point set F of g^S|M is compact and g(F)⊂M, then i_X(g^S,M)≡i_X(g,M) mod p. This theorem can be applied in the theory of asymptotic fixed point theorems: An example may be found at the end of this paper.