Geodesic
Equivalent of the struсtural characteristic of a complex process modeled by algebraical polynomials
Problemy fiziki, matematiki i tehniki, no. 3 (2018), pp. 76-79.

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The equivalence of the generalized modulus of smoothness defined by the generalized shift operator of Jacobi type and the $K$-functional of Petre is proved.
Keywords: generalized Jacobi shift operator, generalized modulus of smoothness, $K$-functional. 
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G. N. Kazimirov. Equivalent of the struсtural characteristic of a complex process modeled by algebraical polynomials. Problemy fiziki, matematiki i tehniki, no. 3 (2018), pp. 76-79. http://geodesic.mathdoc.fr/item/PFMT_2018_3_a12/

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