HADAMARD COMPOSITIONS OF GELFOND-LEONT'EV-SĂLĂGEAN AND GELFOND-LEONT'EV-RUSCHEWEYH DERIVATIVES OF FUNCTIONS ANALYTIC IN THE UNIT DISK.

For analytic functions f (z) = z + Σ^∞_k=2fkzk and g(z) = z + Σ^∞_k=2gkz k=2 k=2 in the unit disk properties of the Hadamard compositions Df [Sf * Dn [s]g and Dn [r] f * Dⁿ_l [R]^g of their Gelfond-Leont'ev-Salagean derivatives Dⁿ_l,]f(z) =z+Σ^∞_k=2 (k) fkzk n and Gelfond-Leont'ev-Ruscheweyh derivatives D_lⁿ[R]f(z) = z + Σ^∞k=2 fkZk ln+k -1 are investigated. For study, generalized orders are used. A connection between the growth of the maximal term of the Hadamard composition of Gelfond-Leont'ev-Saalaagean derivatives or Gelfond-Leont'ev-Ruscheweyh derivatives and the growth of the maximal term of these derivatives of Hadamard composition is established. Similar results are obtained in terms of the classical order and the lower order of the growth. [ABSTRACT FROM AUTHOR]