Abstract: Let C be a closed convex subset of a Banach space X and T: C — C a mapping that satisfies ||Tx - Ty|| =< a||x - y|| + b||Tx -x|| + c||Ty - y|| for all x, y ε C where 0 < a < 1, b => 0, c => 0 and a + b + c = 1. Then T has a unique fixed point. The above theorem, proved by Gregus, is hereby generalized to when X is a metrisable topological vector space. In addition, we are able to use the Mann iteration scheme to approximate the unique fixed point.