Fixed point theory for F-set-contraction multimaps and application to a system of integral inclusions

Abstract

In this paper, we prove some generalizations of Darbo’s fixed point theorem for multivalued mappings by considering a measure of noncompactness which does not necessarily have the maximum property. Moreover, we prove some coupled fixed point theorems for multivalued mappings. Our results generalize, prove and extend well-known results in the subject. An application to solve a nonlinear system of integral inclusions is given.