Some New Results on Bicomplex Bernstein Polynomials

Abstract

The aim of this work is to consider bicomplex Bernstein polynomials attached to analytic functions on a compact C2-disk and to present some approximation properties extending known approximation results for the complex Bernstein polynomials. Furthermore, we obtain and present quantitative estimate inequalities and the Voronovskaja-type result for analytic functions by bicomplex Bernstein polynomials.

Keywords

• bicomplex Bernstein polynomials
• analytic functions
• holomorphic functions
• Voronovskaja-type theorem