Bivariate Bernstein polynomials that reproduce exponential functions

Abstract

In this paper, we construct Bernstein type operators that reproduce exponential functions on simplex with one moved curved side. The operator interpolates the function at the corner points of the simplex. Used function sequence with parameters α and β not only are gained more modeling flexibility to operator but also satisfied to preserve some exponential functions. We examine the convergence properties of the new approximation processes. Later, we also state its shape preserving properties by considering classical convexity. Finally, a Voronovskaya-type theorem is given and our results are supported by graphics.

Keywords

• Bernstein operators
• exponential functions
• classical and exponential convexity
• Voronovskaya-type theorem

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