Fractional monotone approximation theory
Let/∈ Cp ([-1,1]), p ≥ 0 and let L be a linear left fractional differential operator such that L(f) ≥ 0 throughout [0,1]. We can find a sequence of polynomials Qn of degree ≤ n such that L (Qn) ≥ 0 over [0,1], furthermore f is approximated uniformly by Qn. The degree of this restricted approximations is given by an inequalities using the modulus of continuity of f(p).
Indian Journal of Mathematics
Anastassiou, G. (2015). Fractional monotone approximation theory. Indian Journal of Mathematics, 57 (1), 141-149. Retrieved from https://digitalcommons.memphis.edu/facpubs/4710