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We present an estimation of the $H_{k₀,k_r}^{q,\alpha }f$ and $H_{\lambda ,u}^{\varphi ,\alpha }f$ means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.

We present an estimate of the (C,1)(E,1)-strong means with mixed powers of the Fourier series of a function $f\in L_{2\pi }$ as a generalization of the result obtained by M. Yildrim and F. Karakus. Some corollaries on the norm approximation are also given.