  The main object of this paper is to construct a new genuine
Bernstein-Durrmeyer type operators which have better features than the
classical one. Some direct estimates for the modified genuine
Bernstein-Durrmeyer operator by means of the first and second modulus of
continuity are given. An asymptotic formula for the new operator is proved.
Finally, some numerical examples with illustrative graphics have been added to
validate the theoretical results and also compare the rate of convergence.
