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We present upper and lower estimates of the error of approximation of periodic functions by Fejér means in the Lebesgue spacesL    2  π    p{L}_{2{\pi }}^{p}   . The estimates are given in terms of a  K -functional for1  ≤  p  ≤  ∞   1\le p\le \inftyand in terms of the first modulus of continuity in the case1  &lt;  p  &lt;  ∞   1\lt p\lt \infty    . We pay attention to the involved constants.

Direct and strong converse inequalities for approximation with Fejér means