High Order Conformable Fractional Approximation by Max-Product Operators Using Convexity

Abstract

Here we consider the approximation of functions by a large variety of Max-Product operators under conformable fractional differentiability and using convexity. These are positive sublinear operators. Our study relies on our general results about positive sublinear operators. We derive Jackson type inequalities under conformable fractional initial conditions and convexity. So our approach is quantitative by obtaining inequalities where their right hand sides involve the modulus of continuity of a high order conformable fractional derivative of the function under approximation. Due to the convexity assumptions our inequalities are compact and elegant with small constants. It follows Anastassiou (Conformable fractional approximations by max-Product operators using convexity, 2017, [5]).