On the Properties of the Modified λ-Bernstein-Stancu Operators

Abstract

In this study, a new kind of modified (Formula presented.) -Bernstein-Stancu operators is constructed. Compared with the original (Formula presented.) -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.