We give an axiomatic characterization of the fixed point index of an n-valued map. For n-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopy invariance, additivity, and a splitting property. This uniqueness is used to obtain easy proofs of an averaging formula and product formula for the index. In the setting of n-valued maps on a manifold, we show that the axioms can be weakened.
Journal of Fixed Point Theory and Applications
Staecker, Christopher P., "Axioms for the fixed point index of n-valued maps, and some applications" (2018). Mathematics Faculty Publications. 51.
Staecker, P. C. (2018). Axioms for the fixed point index of n-valued maps, and some applications. Journal of Fixed Point Theory and Applications, 20(61). doi:10.1007/s11784-018-0543-4.