Convergence of minimizing sequences

AbstractA functional f defined on a closed convex subset C of a normed space is to be minimized. It is known that if f is strictly convex and C is compact, then any minimizing sequence converges in norm to a unique minimum. A characterization is given herein for the norm convergence of any minimizing sequence when C is weakly compact and f is strictly quasi-convex, a more general result than those which are already known