We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive Voronovskaya-type asymptotic theorem for this type of operator. Then, local global theorems are obtained by using classical modulus continuity K-functional. Finally, rate convergence functions with a derivative bounded variation. The results show that new have g...

The main object of this paper is to construct a new Durrmeyer variant the ?-Bernstein type operators which have better features than classical one. Some results concerning rate convergence in terms first and second moduli continuity asymptotic formulas these are given. Moreover, we define bivariate case investigate approximation degree by means total partial modulus Peetre?s K-functional. A Vor...

Bernstein algebras were introduced by Holgate [6] as an algebraic formulation of the problem of classifying the stationary evolution operators in genetics (see [8]). Since then, many authors have contributed to the study of these algebras, and there is a fairly extensive bibliography on the subject. Known results include classification theorems for sorre types of Bernstein algebras (for instanc...