Titlebook: Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integr; George A. Anastassiou Book 2019 Spri

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Caputo and Canavati Fractional Quantitative Approximation by Choquet Integrals,orovich–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 [.]. We finish with the approximation by the very general direct Choquet-integral form positive sublinear operators.

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,Approximation by a Kantorovich–Shilkret Quasi-interpolation Neural Network Operator,ey are additionally uniformly continuous we derive pointwise and uniform convergences. It follows (Anastassiou, Quantitative approximation by a Kantorovich–Shilkret quasi-interpolation neural network operator (2018) [.]).

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Quantitative Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators,the unit with rates. Additionally, two examples of very general specialized operators are presented fulfilling all the above properties, the higher order of approximation of these operators is also considered. It follows [.].

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,Approximation with Rates by Perturbed Kantorovich–Choquet Neural Network Operators,tion. The right hand sides of our convergence inequalities do not depend on the activation function. It follows (Anastassiou, Quantitative Approximation by Perturbed Kantorovich–Choquet Neural Network Operators (2018) [.]).

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Conformable Fractional Approximation by Choquet Integrals,y the very general direct Choquet-integral form positive sublinear operators. The case of convexity is also studied thoroughly and the estimates become much simpler. All approximations are given via inequalities involving the modulus of continuity of the approximated function’s higher order conformable fractional derivative. It follows [.].