Geodesic
Direct and Inverse Theorems of Approximation Theory for the $m$th Generalized Modulus of Smoothness
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 289-297 
M. K. Potapov. Direct and Inverse Theorems of Approximation Theory for the $m$th Generalized Modulus of Smoothness. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 289-297. http://geodesic.mathdoc.fr/item/TM_2001_232_a23/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The relation between polynomial approximations of functions and their generalized $m$th moduli of smoothness defined with the use of a two-parameter family of nonsymmetric generalized translation operators is examined.

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