In this note we establish some characterizations of (single valued) unctions, that assume values in a Banach space, generating K-Schur concave sums. These results improve some theorems obtained in [13] and [11]. Moreover we prove that a set-valued function is K-concave if and only of it is K-t-concave and K-quasi concave (where t is a fixed number in (0,1)). This result improves the theorems obtained in [11], [2], [5] and extends the theorem of [3]
