Hukuhara’s Topological Degree for non Compact Valued Multifunctions

Abstract

We present a direct construction of a topological degree for multivalued vector fields $I$-$F$ in a Banach space, where $F$ takes closed, bounded, convex (or non convex) values and the set-valued range of $F$ is precompact in the Pompeiu–Hausdorff metric. Some useful properties of our topological degree are established. Applications to fixed point theory including a Borsuk’s type result are considered.