Some inequalities of Jensen type for $Q$-class functions are proved. More precisely a refinement of the inequality f left( frac{1}{P} sum_{i=1}^{n}p_ix_i right) leq P sum_{i=1}^{n} frac{f(x_i)}{p_i} is given in which p_1, ldots, p_n are positive numbers, P= sum_{i=1}^{n}p_i$ and f is a Q -class function. The notion of jointly Q -class function is introduced and some Jensen type inequalities for these functions are proved. Some Ostrowski and Hermite--Hadamard type inequalities related to Q -class functions are presented as well.

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