Let \(D\) be an open convex subset of \(\mathbb{R}^n\), \(Y\) a Banach space with a normal convex cone \(K\) and \(f: D\to Y\) a given function. Then the following conditions are equivalent: \(f\) is \(K\)-Wright-concave; \(f\) generates \(K\)-Schur-concave sums; \(f= A+ V\) with additive \(A\) and concave \(V\); \(f\) is \(K\)-midconcave and \[ f(tx+ (1- t)y)+ f((1- t) x+ ty)\in 2\text{ co}\{f(x), f(y)\}+ K,\;x, y\in D,\;t\in [0, 1]. \] It is also proved that (under some assumptions) a set-valued function is \(K\)-concave iff it is \(K\)-\(t\)-concave and \(K\)-quasiconcave.