In the present paper, we introduce genuine q-Stancu-Bernstein–Durrmeyer operators Znq,α(f;x). We calculate moments of these operators, Znq,α(tj;x) for j=0,1,2, which follows a symmetric pattern. also second order central moment Znq,α((t−x)2;x). give Korovkin-type theorem; estimate rate convergence continuous functions. Furthermore, prove local approximation theorem in terms modulus continuity; ...

An alternative approach, known today as the Bernstein polynomials, to Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated improvements of computational disciplines, we propose a new generalization Bernstein–Kantorovich opera...

In this paper, we use the blending functions of Lupaş type (rational) (p, q)-Bernstein operators based on (p, q)-integers for construction of Lupaş (p, q)-Bézier curves (rational curves) and surfaces (rational surfaces) with shape parameters. We study the nature of degree elevation and degree reduction for Lupaş (p, q)-Bézier Bernstein functions. Parametric curves are represented using Lupaş (p...