One Example in Monotone Approximation Original Research Article

For each non-negative integerna functionf=fnis constructed such thatfhas a continuous and non-negative derivativef′ onI :=[−1, 1] and[formula]whereEn(f′) (E(1)n+1(f)) is the value of the best uniform approximation onIof the functionf′ (f) by arbitrary (monotone onI) algebraic polynomials of degree ⩽n(n+1).