Controllability of mixed Volterra–Fredholm-type integro-differential inclusions in Banach spaces

The paper establishes a sufficient condition for the controllability of semilinear mixed Volterra–Fredholm-type integro-differential inclusions in Banach spaces. We use Bohnenblust–Karlinʹs fixed point theorem combined with a strongly continuous operator semigroup. Our main condition (A5) only depends upon the local properties of multivalued map on a bounded set. An example is also given to illustrate our main results.