On the Properties of the Modified <i>λ</i>-Bernstein-Stancu Operators
Zhi-Peng Lin,
Gülten Torun,
Esma Kangal,
Ülkü Dinlemez Kantar,
Qing-Bo Cai
Affiliations
Zhi-Peng Lin
School of Information Science and Technology, Xiamen University Tan Kah Kee College, Xiamen 363105, China
Gülten Torun
Faculty of Education, Mathematics and Science Education, Kastamonu University, Kastamonu 37210, Türkiye
Esma Kangal
Department of Mathematics, Graduate of Natural and Applied Sciences, Gazi University, Beşevler, Ankara 06500, Türkiye
Ülkü Dinlemez Kantar
Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, Ankara 06500, Türkiye
Qing-Bo Cai
Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
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.
