Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting

DOI10.1515/ms-2017-0063zbMath1505.41005OpenAlexW2777098193MaRDI QIDQ4599380

Danilo Costarelli, Gianluca Vinti

Publication date: 2 January 2018

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ms-2017-0063

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 (12)

A general approximation approach for the simultaneous treatment of integral and discrete operators ⋮ Approximation by truncated Lupaş operators of max-product kind ⋮ Modified neural network operators and their convergence properties with summability methods ⋮ Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression ⋮ Estimates for the neural network operators of the max-product type with continuous and \(p\)-integrable functions ⋮ Approximation results in Orlicz spaces for sequences of Kantorovich MAX-product neural network operators ⋮ The max-product generalized sampling operators: convergence and quantitative estimates ⋮ Asymptotic expansion for neural network operators of the Kantorovich type and high order of approximation ⋮ Extension of saturation theorems for the sampling Kantorovich operators ⋮ Approximation by mixed operators of max-product-Choquet type ⋮ Approximation by max-product operators of Kantorovich type ⋮ Approximation by max-product sampling Kantorovich operators with generalized kernels

Cites Work

• Approximation by max-product neural network operators of Kantorovich type
• Convergence and rate of approximation in \(BV^{\phi}(\mathbb R^N_+)\) for a class of Mellin integral operators
• Saturation and inverse results for the Bernstein max-product operator
• A characterization of absolute continuity by means of Mellin integral operators
• Constructive methods of approximation by ridge functions and radial functions
• Uniform approximation by neural networks
• Approximation by neural networks with a bounded number of nodes at each level
• Some inequalities in classical spaces with mixed norms
• Necessary and sufficient condition for multistability of neural networks evolving on a closed hypercube
• Approximation by neural networks and learning theory
• Nonlinear integral operators with homogeneous kernels: pointwise approximation theorems
• An Integral Upper Bound for Neural Network Approximation
• Degree of Approximation for Nonlinear Multivariate Sampling Kantorovich Operators on Some Functions Spaces
• Universal approximation bounds for superpositions of a sigmoidal function

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