Approximation by Bézier type associated shifted knots of $(\lambda,q)$-Bernstein operators

Abstract

In this article, we introduce the $(\lambda,q)$-Bernstein operators associated with Bézier basis functions using the features of shifted knots. We first construct the $(\lambda,q)$-Bernstein operators using shifted knot polynomials that are connected by a Bézier basis function. We then look into Korovkin's theorem, prove a local approximation theorem, and obtain the convergence theorem for Peetre's $K$-functional and Lipschitz continuous functions. The Voronovskaja type asymptotic formula is finally found in the concluding section of this paper.