On the fixed points of affine nonexpansive mappings

Abstract

Abstract. Let K be a closed convex bounded subset of a Banach space X and let T : K → K be a continuous affine mapping. In this note, we show that (a) if T is nonexpansive then it has a fixed point, (b) if T has only one fixed point then the mapping A = (I + T

A counterexample to the article “On the fixed points of affine nonexpansive mappings”

“…It is easy to show that Tx − T y = x − y , for every x, y in B 1 and also that T is affine. Therefore, the conditions of the main theorem of [2] hold. However, T does not have a fixed point.…”