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- W2083093507 abstract "We consider the Bernstein–Durrmeyer operator M n , ρ with respect to an arbitrary measure ρ on the d -dimensional simplex. This operator is a generalization of the well-known Bernstein–Durrmeyer operator with respect to the Lebesgue measure. We prove that ( M n , ρ f ) ( x ) → f ( x ) as n → ∞ at each point x ∈ supp ρ if f is bounded on supp ρ and continuous at x . Moreover, the convergence is uniform in any compact set in the interior of supp ρ ." @default.
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- W2083093507 date "2014-10-01" @default.
- W2083093507 modified "2023-09-27" @default.
- W2083093507 title "Bernstein–Durrmeyer operators with respect to arbitrary measure, II: Pointwise convergence" @default.
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- W2083093507 doi "https://doi.org/10.1016/j.jmaa.2014.04.006" @default.
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