On the Properties of the Modified λ-Bernstein-Stancu Operators - Lin, Zhi-Peng; Torun, Gülten; Kangal, Esma; Kantar, Ülkü Dinlemez; Cai, Qing-Bo (MDPI AG, 2024)
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.