Abstract

A new subdifferential of a C-lower semicontinuous vector function / from a Banach space X into Rm is defined, where C I Rn is a cone generatedby m linearly independent vectors. Some of its properties are shown. Especially, / is C-quasiconvex (resp. C-convex) if and only if its subdifferential is C-quasimonotone (resp. C-monotone).