# A Nonlinear Extension of Korovkin’s Theorem

@article{Gal2020ANE, title={A Nonlinear Extension of Korovkin’s Theorem}, author={Sorin G. Gal and Constantin P. Niculescu}, journal={arXiv: Classical Analysis and ODEs}, year={2020} }

In this paper we extend the classical Korovkin theorems to the framework of comonotone additive, sublinear and monotone operators. Based on the theory of Choquet capacities, several concrete examples illustrating our results are also discussed.

## 6 Citations

A note on the isotonic vector-valued convex functions.

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The property of isotonicity of a continuous convex function defined on the entire space or only on the positive cone is characterized via subdifferentials. Numerous examples illustrating the obtained…

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In this paper we prove Korovkin type theorems for sequences of sublinear, monotone and weak additive operators acting on function spaces C(X), where X is a compact or a locally compact metric space.…

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Abstract The integral representation of Choquet operators defined on a space C ( X ) is established by using the Choquet-Bochner integral of a real-valued function with respect to a vector capacity.

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We provide a version of Korovkin-type theorems for monotone sublinear operators in vector lattices and discuss the possibilities of further extensions and generalizations. .

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In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their properties, a…

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- MathematicsRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
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The property of isotonicity of a continuous convex function on the positive cone is characterized via subdifferentials. This is used to illustrate a new generalization of the Hardy–Littlewood–Polya…

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