Advanced Ordinary and Fractional Approximation by Positive Sublinear Operators

Abstract

Here we consider the ordinary and fractional approximation of func-
tions by sublinear positive operators with applications to generalized con-
volution type operators expressed by sublinear integrals such as of Cho-
quet and Shilkret ones. The fractional approximation is under fractional
di¤erentiability of Caputo, Canavati and Iterated-Caputo types. We pro-
duce Jackson type inequalities under basic initial conditions. So our way
is quantitative by producing inequalities with their right hand sides in-
volving the modulus of continuity of ordinary and fractional derivatives
of the function under approximation. We give also an application related
to Picard singular integral operators.