Multivalued fixed point theorems in terms of weak topology and measure of weak noncompactness

We present several fixed point theorems for multimaps in Banach spaces, which in turn are multivalued versions of the Mِnch, Daher, Darbo and Sadovskii theorems. The main assumptions of our results are formulated in terms of weak topology and an axiomatic definition of measure of weak noncompactness. Our theorems extend in a broad sense some new and classical results; moreover, a Sadovskii type theorem stated in 2011 is improved.