Abstract
A very general multivariate positive sublinear Choquet integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized operators are presented fulfilling all the above properties, the higher order of multivariate approximation of these operators is also studied. It follows [3].
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Anastassiou, G.A. (2019). Approximation with Rates by Shift Invariant Multivariate Sublinear-Choquet Operators. In: Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators. Studies in Systems, Decision and Control, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-030-04287-5_4
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DOI: https://doi.org/10.1007/978-3-030-04287-5_4
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