Geodesic
On the coincidence of generalized smoothness modules on some class of functions
Problemy fiziki, matematiki i tehniki, no. 2 (2020), pp. 69-70.

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The coincidence of generalized modules of smoothness of order $k$, determined with the help of the generalized shift operator, with different and identical shifts is proved.
Keywords: generalized shift operator, generalized modulus of smoothness. 
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G. N. Kazimirov. On the coincidence of generalized smoothness modules on some class of functions. Problemy fiziki, matematiki i tehniki, no. 2 (2020), pp. 69-70. http://geodesic.mathdoc.fr/item/PFMT_2020_2_a11/

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[3] G.N. Kazimirov, “Ekvivalentnaya strukturnaya kharakteristika dannogo obobschennogo modulya gladkosti”, Problemy fiziki, matematiki i tekhniki, 2010, no. 3(4), 49–51 | MR