Fixed Point Theorems for Decomposable Multi-Valued Maps and Applications

Abstract

We present fixed point theorems for weakly sequentially upper semicontinuous decomposable non-convex-valued maps. They are based on an extension of the Arino–Gautier–Penot Fixed Point Theorem for weakly sequentially upper semicontinuous maps with convex values. Applications are given to abstract operator inclusions in $L^p$ spaces. An example is included to illustrate the theory.