In this paper we will propose a class of generalized Kantorovich type operators constructed using a general differential operator with non-constant coefficients D l g ( x ) = ∑ i = 0 l a i ( x ) g ( i ) ( x ) and its corresponding antiderivative operator I l with respect to the composition D l ◦ I l = I d . The operators studied are of the type K n = D l ◦ L n ◦ I l where L n are positive linear operators. For these operators we will prove an approximation result and a Voronovskaja type theorem. Also, a simultaneous approximation result will be provided for a particular case. The operators studied in this paper are linear but not positive operators.