On the Properties of the Modified <i>λ</i>-Bernstein-Stancu Operators

Abstract

In this study, a new kind of modified λ-Bernstein-Stancu operators is constructed. Compared with the original λ-Bézier basis function, the newly operator basis function is more concise in form and has certain symmetry beauty. The moments and central moments are computed. A Korovkin-type approximation theorem is presented, and the degree of convergence is estimated with respect to the modulus of continuity, Peetre’s K-functional, and functions of the Lipschitz-type class. Moreover, the Voronovskaja type approximation theorem is examined. Finally, some numerical examples and graphics to show convergence are presented.

Keywords

• λ-Bernstein-Stancu type operators
• Bézier Bases functions
• Korovkin type theorem
• modulus of continuity
• rate of approximation
• Voronovskaja type theorem