Convergence for a family of neural network operators in Orlicz spaces

DOI10.1002/mana.201600006zbMath1373.47010OpenAlexW2502087804MaRDI QIDQ2965304

Danilo Costarelli, Gianluca Vinti

Publication date: 2 March 2017

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201600006

zbMATH Keywords

Orlicz spacesigmoidal functionmodular convergenceneural network operator

Mathematics Subject Classification ID

Linear operator approximation theory (47A58) Rate of convergence, degree of approximation (41A25) Approximation by operators (in particular, by integral operators) (41A35) Approximation by other special function classes (41A30)

Related Items (28)

Approximation theorems for a family of multivariate neural network operators in Orlicz-type spaces ⋮ Voronovskaja type theorems and high-order convergence neural network operators with sigmoidal functions ⋮ On the approximation by single hidden layer feedforward neural networks with fixed weights ⋮ Event-triggered \(\mathcal H_\infty\) state estimation for semi-Markov jumping discrete-time neural networks with quantization ⋮ A characterization of the absolute continuity in terms of convergence in variation for the sampling Kantorovich operators ⋮ Saturation classes for MAX-product neural network operators activated by sigmoidal functions ⋮ Modified neural network operators and their convergence properties with summability methods ⋮ Novel bifurcation results for a delayed fractional-order quaternion-valued neural network ⋮ Nonlinear approximation via compositions ⋮ Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression ⋮ Approximation by Kantorovich form of modified Szász-Mirakyan operators ⋮ Detection of thermal bridges from thermographic images by means of image processing approximation algorithms ⋮ A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces ⋮ Computing the Approximation Error for Neural Networks with Weights Varying on Fixed Directions ⋮ Direct, inverse, and equivalence theorems for weighted Szász-Durrmeyer-Bézier operators in Orlicz spaces ⋮ Inverse results of approximation and the saturation order for the sampling Kantorovich series ⋮ 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 ⋮ Deep Network Approximation Characterized by Number of Neurons ⋮ 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 ⋮ Modified Bernstein-Kantorovich operators for functions of one and two variables ⋮ Quantitative estimates involving K-functionals for neural network-type operators ⋮ Convergence of sampling Kantorovich operators in modular spaces with applications ⋮ Relative uniform convergence of a sequence of functions at a point and Korovkin-type approximation theorems ⋮ Extension of saturation theorems for the sampling Kantorovich operators ⋮ Approximate solutions of Volterra integral equations by an interpolation method based on ramp functions ⋮ Approximation by max-product sampling Kantorovich operators with generalized kernels

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