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In this paper, for a generalised shift operator introduced earlier, we prove theorem of coincidence of classes of functions defined by the order of best approximation by algebraical polynomials and the generalised Lipschitz classes defined by the generalised shift operator. Mathematics Subject Classification: Primary 41A35, Secondary 41A50, 42A16 Keywords: Generalised modulus of smoothness, asymmetric generalised shift operator, theorem of coincidence of classesdoi:10.12988/ijma.2013.13001 fatcat:accnasqvnffatcqqs35sm3f4ri