A nonlinear extension of Korovkin's theorem

DOI10.1007/s00009-020-01583-7OpenAlexW3080183003MaRDI QIDQ2199751

Constantin P. Niculescu, Sorin Gheorghe Gal

Publication date: 14 September 2020

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.00002

zbMATH Keywords

monotone operatorChoquet integralKorovkin theoremsublinear operatorcomonotone additivity

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximation by operators (in particular, by integral operators) (41A35) Approximation by positive operators (41A36)

Related Items (10)

An operator version of the Korovkin theorem ⋮ Iterates of monotone and sublinear operators on spaces of continuous functions ⋮ Korovkin-type theorems for weakly nonlinear and monotone operators ⋮ Nonlinear operator extensions of Korovkin's theorems ⋮ Quantitative Korovkin theorems for monotone sublinear and strongly translatable operators in $L_{p}([0, 1)$, $1\le p\le \infty $] ⋮ Korovkin-type theorems for statistically convergent sequences of monotone and sublinear operators ⋮ Choquet operators associated to vector capacities ⋮ A note on the Choquet type operators ⋮ Nonlinear versions of Korovkin's abstract theorems ⋮ Infimal generators and monotone sublinear operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Set functions, games and capacities in decision making
• Stochastic finance. An introduction in discrete time.
• Uniform and pointwise convergence of Bernstein-Durrmeyer operators with respect to monotone and submodular set functions
• Allocations of probability
• Signed integral representations of comonotonic additive functionals
• Choquet integrals in potential theory
• Non-additive measure and integral
• Korovkin-type approximation theory and its applications
• Uniform and pointwise quantitative approximation by Kantorovich-Choquet type integral operators with respect to monotone and submodular set functions
• A note on Korovkin test families
• Theorems of Korovkin type for adapted spaces
• Note on a generalized Bohman-Korovkin theorem
• Theory of capacities
• Generalized Measure Theory
• Integral representation of continuous comonotonically additive functionals
• Kantorovich's Mass Transport Problem for Capacities
• Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
• An Overview of Absolute Continuity and Its Applications
• Korovkin-type Theorems and Approximation by Positive Linear Operators

This page was built for publication: A nonlinear extension of Korovkin's theorem