An interpolatory version of Timan's theorem on simultaneous approximation (Q1187273)

Let \(f\in C^ q[-1,1]\). A result of Timan states the existence of a sequence of polynomials \(\{P_ n\}\) such that \[ | f(x)-P_ n(x)|=O\left\{\left({\sqrt{1-x^ 2} \over n}+{1\over n^ 2}\right)^ q \omega\left( f^{(q)}; {\sqrt{1-x^ 2} \over n}+{1\over n^ 2}\right)\right\}, \] where \(\omega(\cdot)\) denotes the modulus of continuity. The authors prove that the sequence \(\{P_ n\}\) may be found satisfying additionally some interpolatory properties.