Blending type approximation by $\lambda$-Bernstein-Beta type operators

Abstract

We propose a blending type generalized Bernstein-Beta operators associated with B\'{e}zier bases $\tilde{q}_{k,l}(\lambda;y)$ and a shape parameter $\lambda$. First, we study the convergence results for the proposed operators and then establish their rate of convergence with the help of the modulus of continuity and Peetre's K-functional. Next, we present quantitative Voronovskaja-type results to study their approximation speed. In addition, we estimate the error for absolutely continuous mappings possessing derivatives of bounded variation.