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...

For the qualitative results of pointwise and uniform approximation obtained in [10], we present general quantitative estimates in terms of the modulus of continuity and in terms of a K-functional, for the generalized multivariate Bernstein-Durrmeyer operator Mn,Γn,x , written in terms of the Choquet integral with respect to a family of monotone and submodular set functions, Γn,x, on the standar...

The main purpose of this article is to study the bivariate approximation generalization for Baskakov-Durrmeyer-operators with aid non-negative parametric variants suppose 0 ? ?1,?2 1. We obtain order by use modulus continuity in terms well known Peetre?s K-functional, Voronovskaja type theorems and Lipschitz maximal functions. Further, we also discuss here properties operators B?gel-spaces mixe...

We propose certain Durrmeyer-type operators for Apostol-Genocchi polynomials in this research. We explore these operators' approximation attributes and measure the rate of convergence. In addition, we present a direct theorem based on first second-order modulus continuity, local findings Lipschitz class functions typical continuity. Finally, showed graph illustratin...