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arXiv · 2405.16935

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

Laura Angeloni·Danilo Costarelli·Chiara Darielli
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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.

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Laura Angeloni, Danilo Costarelli, Chiara Darielli. 2024-05-27. Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube. https://arxiv.org/abs/2405.16935

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