On the Homotopy Property of Nussbaum's Fixed Point Index

Abstract

In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.