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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     author = {M. K. Potapov and G. N. Kazimirov},
     title = {Polynomial approximation of functions with given order of the $k$th generalized modulus of smoothness},
     journal = {Matemati\v{c}eskie zametki},
     pages = {425--436},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a13/}
}
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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/