Mixed Conformable and Iterated Fractional Approximation by Choquet Integrals

We analyse the approximation of the unit operator by positive sublinear operators of quantitative mixed conformable and iterated fractional type, including a precise Choquet integral interpretation of these operators. First of all, we examine the mixed conformable and iterated fractional rate of convergence of both the Bernstein-Kantorovich-Choquet operator and the Bernstein-Durrweyer-Choquet polynomial Choquet-integral operator. Next we use a representation theorem due to Schmeidler (1986) [1] in order to study some very general comonotonic positive sublinear operators. Finally, we give an approximation using some very general direct Choquet-integral form positive sublinear operators. The approximations of mixed conformable and iterated fractional type are given as inequalities which involve the modulus of continuity of the approximated function and its mixed conformable and iterated fractional derivatives