Belonging to convergence classes of Hadamard compositions of Gelfond-Leont'ev derivatives for analytic functions

  • O.M. Mulyava National University of Food Technologies, 68 Volodymyrska str., 01601, Kyiv, Ukraine
  • M.M. Sheremeta Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
Keywords: entire function, analytic function in the unit disk, Gelfond-Leont'ev derivative, Hadamard composition
Published online: 2012-06-28


The conditions are found, under which the belonging to Valiron convergence class of entire functions $f$ and $g$ implies the belonging to this class of Gelfond-Leont'ev derivative of Hadamard composition of functions $f$ and $g$ and of Hadamard composition of Gelfond-Leont'ev derivatives of these functions. Analogous problem is solved for analytic functions in the unit disk.