Uniform and pointwise convergence of Bernstein-Durrmeyer operators with respect to monotone and submodular set functions

DOI10.1016/J.JMAA.2014.12.012zbMath1305.41028OpenAlexW2017604269MaRDI QIDQ482772

Bogdan D. Opris, Sorin Gheorghe Gal

Publication date: 6 January 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.12.012

zbMATH Keywords

uniform convergenceChoquet integralpointwise convergenceBernstein-Durrmeyer operatormonotone and submodular set function

Mathematics Subject Classification ID

Approximation by positive operators (41A36)

Related Items (10)

Uniform and pointwise quantitative approximation by Kantorovich-Choquet type integral operators with respect to monotone and submodular set functions ⋮ Quantitative estimates in \(L^{p}\)-approximation by Bernstein-Durrmeyer-Choquet operators with respect to distorted Borel measures ⋮ Iterates of monotone and sublinear operators on spaces of continuous functions ⋮ A nonlinear extension of Korovkin's theorem ⋮ Quantitative Korovkin theorems for monotone sublinear and strongly translatable operators in $L_{p}([0, 1)$, $1\le p\le \infty $] ⋮ Quantitative Estimates for $L^p$-Approximation by Bernstein-Kantorovich-Choquet Polynomials with Respect to Distorted Lebesgue Measures ⋮ Approximation properties of mixed sampling-Kantorovich operators ⋮ Volterra-Choquet nonlinear operators ⋮ Quantitative approximation by nonlinear Picard-Choquet, Gauss-Weierstrass-Choquet and Poisson-Cauchy-Choquet singular integrals ⋮ Approximation by mixed operators of max-product-Choquet type

Cites Work

• Approximation by multivariate Bernstein-Durrmeyer operators and learning rates of least-squares regularized regression with multivariate polynomial kernels
• Uniform convergence of Bernstein-Durrmeyer operators with respect to arbitrary measure
• Bernstein-Durrmeyer operators with respect to arbitrary measure. II: Pointwise convergence
• Multivariate Bernstein-Durrmeyer operators with arbitrary weight functions
• Default reasoning and possibility theory
• Non-additive measure and integral
• Theory of capacities
• Generalized Measure Theory

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