Conformable Fractional Approximation by Choquet Integrals

Abstract

Here we present the conformable fractional quantitative 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 conformable fractional rate of the convergence of the well-known Bernstein–Kantorovich–Choquet and Bernstein–Durrweyer–Choquet polynomial Choquet-integral operators. Then we study in the fractional sense the very general comonotonic positive sublinear operators based on the representation theorem of Schmeidler [12]. We continue with the conformable fractional approximation by 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 [5].