Abstract
In this paper we extend Korovkin’s theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function spaces. Several examples illustrating the theory are included.
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Acknowledgements
The authors would like to thank the reviewers for a number of valuable suggestions and for pointing out some minor typos in an earlier version of this paper.
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SG. and C.N. wrote the main manuscript text and both prepared the final version. All authors reviewed the manuscript.
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Gal, S.G., Niculescu, C.P. Nonlinear operator extensions of Korovkin’s theorems. Positivity 28, 14 (2024). https://doi.org/10.1007/s11117-024-01034-7
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DOI: https://doi.org/10.1007/s11117-024-01034-7
Keywords
- Korovkin type theorems
- Monotone operator
- Sublinear operator
- Weakly nonlinear operator
- Ordered Banach space
- Choquet’s integral