Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube

2024/05/27 by Angeloni, Laura, Costarelli, Danilo, Darielli, Chiara
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2405.16935

Abstract

In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube [0, 1]^d and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its square. In particular, we prove uniform convergence, by means of two different approaches, as well as a quantitative estimate of the order of approximation in terms of the modulus of continuity of the approximated function.

Related

• Multivariate polynomial approximation in the hypercube
• Extremal Polynomials and Entire Functions of Exponential Type
• (p,q)-Beta Functions and Applications in Approximation
• On approximation of functions by polynomials and by entire functions of exponential type
• On the rates of pointwise convergence for Bernstein polynomials