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Caputo and Canavati Fractional Quantitative Approximation by Choquet Integrals

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Book cover Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 190))

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Abstract

Here we consider the quantitative Caputo and Canavati fractional approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the study of the fractional rate of the convergence of the well-known Bernstein–Kantorovich–Choquet and Bernstein–Durrweyer–Choquet polynomial Choquet-integral operators. Then we study the very general comonotonic positive sublinear operators based on the representation theorem of Schmeidler [18]. We finish with the approximation by the very general direct Choquet-integral form positive sublinear operators.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

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  1. George A. Anastassiou
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Correspondence to George A. Anastassiou .

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Anastassiou, G.A. (2019). Caputo and Canavati Fractional Quantitative Approximation by Choquet Integrals. 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_9

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