In this paper we characterize multi-Jensen functions f : $V^n;{ ightarrow};W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $mathbb{R};{ ightarrow};mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $mathbb{R};{ ightarrow};mathbb{R}$) such that the Jensen difference $$2f;(frac{x;+;y}{2});-;f(x);-;f(y)$$ (respectively, the Pexider difference $$2f;(frac{x;+;y}{2});-;g(x);-;h(y))$$ takes values in a countable subgroup of $mathbb{R}$.