The proof of direct and inverse theorems of the approximation theory for the generalized modulus of smoothness is the aim of the paper. Direct and inverse theorems of the approximation theory have been obtained for moduluses of smoothness, determined with the help of operators of a generalized shift of Jakobi type and of Chebyshev - Jakobi type. Intervals of the weight variation for the spaces considered, in which these theorems are correct, have been found. The paper results may find their field of application in the theory of functions and calculation mathematicsAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio
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