Coincidence of relatively expansive maps

Abstract

Let C be a  bounded closed convex subset of a uniformly convex Banach space, and let f and g be selfmaps of C such that f is expansive relative to g. Without assuming compactness of C, we show that f and g have coincidence points,  and  they have common fixed points if they commute. As a consequence, we derive the fixed point theorem of Browder-Göhde-Kirk.