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>

Abstract

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.

Keywords

• Bernstein operators
• statistical convergence
• <i>q</i>-integers
• basis function
• modulus of continuity