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This note presents the proof of the monotonicity property for the sequence of Stancu type polynomials, involving divided differences and convex functions. As an application we get the form of remainder term associated to the Stancu type operators applying the Popoviciu’s Theorem.

In the present paper the author revises some known results, respectively establishes new results for Bernstein-Stancu operators and for a particular case of the same operators, introduced first by L. Lupas¸ and A. Lupas¸.

The paper presents the generalized form of the Bernstein operator associated with any real-valued function {f\colon[a,b]\to\mathbb{R}}. For this generalized Bernstein operator, we study the qualitative and quantitative aspects concerning uniform convergence, order of approximation and asymptotic behavior.