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

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arxiv 2405.16935 v1 pith:NTTX3TKV submitted 2024-05-27 math.CA math.FA

Laura Angeloni , Danilo Costarelli , Chiara Darielli This is my paper · ORCID
classification math.CAmath.FA
keywords approximationexponentialbernstein-typefunctionhypercubemultidimensionalpolynomialsapproaches
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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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  1. Advancements in nonlinear exponential sampling: convergence, quantitative analysis and Voronovskaya-type formula

    math.FA 2024-11 accept novelty 6.0 of 10

    A nonlinear exponential Kantorovich sampling operator is introduced, with convergence theorems, quantitative error bounds, and a Voronovskaja-type formula in Mellin-Orlicz spaces.

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