In order to find a relationship with the Bernstein operators of the second kind introduced by P. Soardi, the author defines two classes of generalized convex functions, weakening the property of convexity that is linked to the classical Bernstein operators. The first class \(K_2\) is defined via the divided differences of a function \(f\in C[0,1]\) at some particular points, while the functions in the class \(K_3\) should satisfy an inequality involving the first and second derivative. Under regularity assumptions, \(K_2\subset K_3.\) In the main result, the author shows that the functions in \(K_2\) and \(K_3\) are related to the Bernstein operators of second kind, proving that they satisfy some inequalities involving these operators.