# References for a proof of a Jackson's inequality?

Let $$g:[0,2\pi]\to \mathbb{C}$$ which is $$\mathcal{C}^k([0,2\pi],\mathbb{R})$$ and periodic. If $$\mid f^{(k)}(x) \mid\le 1$$ then for each $$n\in \mathbb{N}^*$$, there exists a trigonometric polynomial $$T_{n-1}$$ of degree at most $$n-1$$ such that : $$\forall x\in [0,2\pi]$$, $$\mid g(x)-T_{n-1}(x)\mid \le \frac{\Delta_k}{n^k}$$, where $$\Delta_k$$ depends only on $$k$$.

I was wondering if someone had references for the proof of this statement. I looked at the book of Achieser "Theory of Aprroximation" but I found that the proof was difficult to follow...