KRASNOSEL’SKII FIXED POINT THEOREMS INVOLVING A CLASS OF CONVEX-POWER CONDENSING MULTIVALUED MAPPINGS

In this paper, we use a class of convex-power condensing mappings with respect to a measure of weak noncompactness in Banach spaces in order to present a new Krasnosel’skii fixed point theorem for multivalued mappings which have sequentially closed graph. We prove also a new version of Leary-Schauder type results. We apply these results to investigate the existence of weak solution to a Volterrra integral inclusion of Krasnosel’skii type in a non reflexive Banach space.