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In this paper, we discuss the rate of the approximation by matrix transform means of Fourier series with respect to the character system of the group of 2-adic integers inLp⁢(I){L^{p}(I)}spaces (1≤p&lt;∞{1\leq p&lt;\infty}) and inC⁢(I){C(I)}. Moreover, we give an application for functions in Lipschitz classesLip⁢(α,p,I){\mathrm{Lip}(\alpha,p,I)}(α&gt;0{\alpha&gt;0},1≤p&lt;∞{1\leq p&lt;\infty}) andLip⁢(α,C⁢(I)){\mathrm{Lip}(\alpha,C(I))}(α&gt;0{\alpha&gt;0}).

Approximation by matrix transform means with respect to the character system of the group of 2-adic integers