Genuine modified Bernstein-Durrmeyer operators.

The present paper deals with genuine Bernstein-Durrmeyer operators which preserve some certain functions. The rate of convergence of new operators via a Peetre [Formula: see text]-functional and corresponding modulus of smoothness, quantitative Voronovskaya type theorem and Grüss-Voronovskaya type theorem in quantitative mean are discussed. Finally, the graphic for new operators with special cases and for some values of n is also presented.