Statistical approximation properties of λ-Bernstein operators based on q-integers

Abstract

In this paper, we introduce a new generalization of λ-Bernstein operators based on q-integers, we obtain the moments and central moments of these operators, establish a statistical approximation theorem and give an example to show the convergence of these operators to f(x). It can be seen that in some cases the absolute error bounds are smaller than the case of classical q-Bernstein operators to f(x).

Keywords

• q-integers
• λ-bernstein operators
• statistical convergence
• basis function
• 41a10
• 41a25
• 41a36