Abstract
It is proved that if the increasing sequence (np) of natural numbers satisfies the condition np+1/np → 1 (p → ∞) and all derivatives f(np) of the analytic function f in D={z:¦z¦<1} are univalent in D, then f is an entire function. At the same time, for each increasing sequence (np) natural numbers such that np+1/np → ∞ (p → ∞) there exists an analytic function f in D all of whose derivatives f(np) are univalent in D and ∂D is the boundary for f. The growth of entire functions with derivatives univalent in the disc D is also studied.
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