A FIXED POINT THEOREM FOR MONOTONE MULTIVALUED MAPPINGS IN ORDERED METRIC SPACES AND APPLICATION

Abstract

Let $(X,d,⪯)$ be a complete ordered metric space. We present a fixed point existence theorem for monotone multivalued mappings $T:X\to 2^X$ under the assumption of Sadovskii: $\mu (T\mathrm{\Omega })<\mu (\mathrm{\Omega })$ for every bounded subset $\mathrm{\Omega }$ of $X$, where $\mu$ is a measure of noncompactness on $X$. As an application, we show the existence of solutions for a specific class of functional integral inclusions.