Abstract
In this paper we prove analogs of Korovkin’s theorem in the context of weakly nonlinear and monotone operators acting on Banach lattices of functions of several variables. Our results concern the convergence almost everywhere, the convergence in measure and the convergence in \(L^{p}\)-norm. Several results illustrating the theory are also included.
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Gal, S.G., Niculescu, C.P. Korovkin-Type Theorems for Weakly Nonlinear and Monotone Operators. Mediterr. J. Math. 20, 56 (2023). https://doi.org/10.1007/s00009-023-02271-y
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DOI: https://doi.org/10.1007/s00009-023-02271-y
Keywords
- Korovkin-type theorems
- monotone operator
- sublinear operator
- convergence almost everywhere
- convergence in measure
- convergence in \(L^{p}\)-norm
- choquet’s integral