Better numerical approximation by λ-Durrmeyer-Bernstein type operators

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 Voronovskaja Gr?ss-Voronovskaja theorem for also proven. Further, introduce associated GBS (Generalized Boolean Sum) determine order with aid mixed smoothness B?gel continuous differentiable functions. Finally theoretical analyzed numerical examples.