FIXED POINTS OF SUMS OF NONEXPANSIVE MAPS AND COMPACT MAPS

Let X be a Banach space satisfying Opial's condition, C a weakly compact convex subset of $X,F:C{\rightarrow}X$ a nonexpansive map, and let $G:C{\rightarrow}X$ be a compact and demiclosed map. We prove that F + G has a fixed point in C if $F+G:C{\rightarrow}X$ is a weakly inward map.