Approximation by the modified λ-Bernstein-polynomial in terms of basis function

Abstract

In this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin's theorem, establish a local approximation theorem, and provide a convergence theorem for Lipschitz continuous functions and Peetre's $ K $-functional. In addition, we also obtain an asymptotic formula of the type Voronovskaja.

Keywords

• bernstein-polynomial
• $ \lambda $-bernstein-polynomial
• bézier basis function
• shifted knots
• modulus of continuity
• lipschitz maximal functions
• peetre's $ k $-functional