A generalization of Nadler's fixed point theorem and its application (Q367301)

The authors generalize the well-known Nadler's fixed point theorem and apply their results to integral inclusions. The first main result is a fixed point theorem for multivalued \(H^+\) contractions. In Section~4, they introduce the notion of \(H^+\) -type nonexpansive mapping and extend some fixed point results in this case. In the last section, a nonconvex integral inclusion is considered and the authors prove a Filippov type existence theorem by using an appropriate norm on the space of selections of the multifunction and an \(H^+\)-type contraction for set-valued maps.