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Let  G  be a doubly connected domain in the complex plane    $$\mathbb {C}$$  C , bounded by Ahlfors 1-regular curves. In this study the approximation of the functions by Faber–Laurent rational functions in the    $$\omega $$  ω -weighted generalized grand Smirnov classes    $$\mathcal {E}^{p),\theta }(G,\omega )$$  E p ) , θ ( G , ω ) in the term of the  r th   $$,~r=1,2\ldots ,$$  , r = 1 , 2 … , mean modulus of smoothness are investigated.

On approximation of functions by rational functions in weighted generalized grand Smirnov classes