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Differential subordination and Bazilevič functions. (English) Zbl 0859.30024

Let p, λ, h and ϕ be analytic functions in the unit disc Δ. In this paper, the author proves that, under suitable assumptions on the above functions, the following relation holds: p(z)+λ(z)zp ' (z)h(z) implies p(z)ϕ(z)h(z) for zΔ, where denotes the subordination of functions.

Basing himself on this result he proves a sufficient condition for an analytic function to be starlike in Δ. These results are some extensions of the classical result of Sakaguchi and Libera.

30C80Maximum principle; Schwarz’s lemma, Lindelöf principle, etc. (one complex variable)
30C45Special classes of univalent and multivalent functions
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