Approximation by Bézier type associated shifted knots of (λ, q)-Bernstein operators

In this article, we introduce the (?, q)-Bernstein operators associated with B?zier basis functions using the features of shifted knots. We first construct the (?, q)-Bernstein operators using shifted knot polynomials that are connected by a B?zier 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.