Uniform convergence and rate of approximation for a nonlinear version of the generalized sampling operator

DOI10.1007/BF03322053zbMath0932.41017MaRDI QIDQ1281425

Gianluca Vinti, Carlo Bardaro

Publication date: 21 March 2000

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

zbMATH Keywords

order of approximationapproximate identitynonlinear integral operator

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Iterative procedures involving nonlinear operators (47J25) Linear operator approximation theory (47A58) Rate of convergence, degree of approximation (41A25) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (4)

Rates of approximation for general sampling-type operators in the setting of filter convergence ⋮ Quantitative estimates for nonlinear sampling Kantorovich operators ⋮ On the approximate form of Kluvánek's theorem ⋮ Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing

Cites Work

• Approximation formulae of Voronovskaya-type for certain convolution operators
• The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis
• On approximation properties of certain non-convolution integral operators
• The sampling theorem and linear prediction in signal analysis
• Approximation of continuous and discontinuous functions by generalized sampling series
• Nonlinear operators of integral type in some function spaces
• Errors in truncated sampling series with measured sampled values for non-necessarily bandlimited functions
• On the order of modular approximation for nets of integral operators in modular Lipschitz classes
• Modular convergence theorems in fractional Musielak-Orlicz spaces
• On the precision of uniform approximation of continuous functions by certain linear positive operators of convolution type
• Modular convergence in generalized orlicz spaces for moment type operators
• Sampling Theory for not Necessarily Band-Limited Functions: A Historical Overview
• A general approach to the convergence theorems of generalized sampling series
• Approximation by nonlinear integral operators in some modular function spaces
• Modular estimates for nonlinear integral operators and applications in fractional calculus
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