Some Statistical and Direct Approximation Properties for a New Form of the Generalization of <i>q</i>-Bernstein Operators with the Parameter <i>λ</i>
Lian-Ta Su,
Esma Kangal,
Ülkü Dinlemez Kantar,
Qing-Bo Cai
Affiliations
Lian-Ta Su
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
Esma Kangal
Department of Mathematics, Graduate School 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 different generalization of q-Bernstein operators with the parameter λ∈[−1,1] is created. The moments and central moments of these operators are calculated, a statistical approximation result for this new type of (λ,q)-Bernstein operators is obtained, and the convergence properties are analyzed using the Peetre K-functional and the modulus of continuity for this new operator. Finally, a numerical example is given to illustrate the convergence behavior of the newly defined operators.
