A minimization theorem for a set-valued mapping

In this paper, a new minimization theorem is obtained for a set-valued mapping and an equivalent relation between a variant of Ekeland variational principle [T.X.D. Ha, Some variants of Ekeland variational principle for a set-valued map, J. Optim. Theory Appl. 124 (1) (2005) 187–206] and the minimization theorem is established.