Geodesic
On the connection between a~$r$-order modulus of smoothness and the~best approximation by algebraic polynomials
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 563-587

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In this paper an asymmetrical operator of generalized translation is introduced and used to define the generalized modulus of smoothness; the direct and inverse theorems in approximation theory are proved for that modulus. 
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     author = {M. K. Potapov and F. M. Berisha},
     title = {On the connection between a~$r$-order modulus of smoothness and the~best approximation by algebraic polynomials},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {563--587},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a12/}
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M. K. Potapov; F. M. Berisha. On the connection between a~$r$-order modulus of smoothness and the~best approximation by algebraic polynomials. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 2, pp. 563-587. http://geodesic.mathdoc.fr/item/FPM_1999_5_2_a12/