Caputo and Canavati Fractional Quantitative Approximation by Choquet Integrals

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.