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

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

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 d...

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Veröffentlicht in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2025-01, Vol.119 (1), Article 28
Hauptverfasser: Angeloni, Laura, Costarelli, Danilo, Darielli, Chiara
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Approximation
Convergence
Exponential functions
Hypercubes
Operators (mathematics)
Polynomials
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description 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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subjects Approximation
Convergence
Exponential functions
Hypercubes
Operators (mathematics)
Polynomials
title Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube
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