Remarks to properties of analytic in the unit disc functions P-valent along with their derivatives

Abstract

Let K = ( k j ) be an increasing sequence of integers, k 0 = 0 , and E ( K ) be a class of analytic in the disk D = { z : | z | < 1 } functions f such that for some p ∈ N all derivatives f ( k j ) are in the middle p -valent in D . It is proved that every function f ∈ E ( K ) is entire if and only if