In this note, we will give an estimation of the pointwise orders of approx-imation of functions and their derivatives by Hermite interpolation based on the roots of the first kind Chebychev polynomials. The results answer a problem posed by Xie Tingfan in [4].
Let X be a strictly convex complex Banach space, B be its unit ball and f: B→B be F-differentiable, if f(0)=0, then f has the same fixed point set with Dr(0) in B. In particular, the fixed point set for f is ffine.
