Geodesic
Polynomial approximation of functions with given order of the $k$th generalized modulus of smoothness
Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 425-436.

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The problem of approximation by algebraic polynomials is considered on function classes characterized by the value of the $k$th generalized modulus of smoothness defined by the Jacobi generalized shift operator. 
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M. K. Potapov; G. N. Kazimirov. Polynomial approximation of functions with given order of the $k$th generalized modulus of smoothness. Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 425-436. http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a13/

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