Relative topological degree of set-valued compact vector fields and its applications

The authors define a concept of relative topological degree of set-valued compact vector fields with respect to a closed convex subset in a locally convex topological vector space. Using this concept, they extend the concept of degree of ultimately compact vector fields introduced by Sadovskii and generalized by Petryshyn and Fitzpatrick. The authors also establish a fixed point theorem of the Kakutani-Fan type and a generalized Borsuk fixed point theorem for ultimately compact operators.