Embedding cones in hyperspaces

Given a metric continuum X, let C(X) be the hyperspace of subcontinua of X and Cone(X) the topological cone of X. We say that a continuum X is cone-embeddable in C(X) provided that there is an embedding h from Cone(X) into C(X) such that h(x,0)={x} for each x in X. In this paper, we present some results concerning continua X that are cone-embeddable in C(X).