Approximation results in Orlicz spaces for sequences of Kantorovich MAX-product neural network operators

DOI10.1007/s00025-018-0799-4zbMath1390.41019arXiv1912.00911OpenAlexW3104090361MaRDI QIDQ1743222

Danilo Costarelli, Anna Rita Sambucini

Publication date: 13 April 2018

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.00911

zbMATH Keywords

Orlicz spacesigmoidal functionK-functionalmodular convergenceMAX-product neural network operator

Mathematics Subject Classification ID

Linear operator approximation theory (47A58) Interpolation in approximation theory (41A05) Rate of convergence, degree of approximation (41A25) Approximation by other special function classes (41A30)

Related Items (24)

DENSITY RESULTS BY DEEP NEURAL NETWORK OPERATORS WITH INTEGER WEIGHTS ⋮ Some new theorems on the approximation of maximum product type of multivariate nonlinear Bernstein-Chlodowsky operators ⋮ Some applications of modular convergence in vector lattice setting ⋮ Asymptotic expansions and Voronovskaja type theorems for the multivariate neural network operators ⋮ Nonlinear approximation via compositions ⋮ Quantitative estimates for neural network operators implied by the asymptotic behaviour of the sigmoidal activation functions ⋮ Approximation error for neural network operators by an averaged modulus of smoothness ⋮ Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression ⋮ Some density results by deep Kantorovich type neural network operators ⋮ Approximation by pseudo-linear discrete operators ⋮ A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces ⋮ Approximation by max-min operators: a general theory and its applications ⋮ Direct, inverse, and equivalence theorems for weighted Szász-Durrmeyer-Bézier operators in Orlicz spaces ⋮ On a Durrmeyer-type modification of the exponential sampling series ⋮ Deep Network Approximation Characterized by Number of Neurons ⋮ The max-product generalized sampling operators: convergence and quantitative estimates ⋮ Quantitative estimates for nonlinear sampling Kantorovich operators ⋮ Approximate solutions of Volterra integral equations by an interpolation method based on ramp functions ⋮ Approximation by mixed operators of max-product-Choquet type ⋮ Approximation by max-product operators of Kantorovich type ⋮ On approximation by max-product Shepard operators ⋮ Approximation by max-product sampling Kantorovich operators with generalized kernels ⋮ Max-product type multivariate sampling operators and applications to image processing ⋮ Approximation by Kantorovich-type max-min operators and its applications

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