Linear 2-normed space is a generalization of linear normed space

which defines a more extensive norm. In this paper

we get contraction mapping theorem in linear 2-normed space holds

and the set of fixed points for nonexpansive mapping is convex when linear 2-normed space is strictly convex. We obtain that the strictly convex linear 2-normed space with finite dimension is uniformly convex. Thus we get the corollary that the linear 2-normed space induced by the vector product is uniformly convex.