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.
Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube
Angeloni, Laura
;Costarelli, Danilo;Darielli, Chiara
2025
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.File in questo prodotto:
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