Some theorems on subordination by univalent functions. (English) Zbl 0591.30010

Obradović, Milutin

Mat. Vesn. 37, 211-214 (1985).

Let us denote by \(\bar S^*(\alpha)\) the class of regular functions which satisfy the condition \[ Re zf'(z)/(f(z)-f(-z))>\alpha \quad for\quad | z| <1,\quad \alpha \in [0,]. \] By \(B_ 1(\alpha)\) we shall denote the class of regular functions satisfying the condition \[ Re zf'(z)f^{\alpha -1}(z)/z^{\alpha}>0\quad for\quad | z| <1\quad and\quad \alpha >0. \] In this paper a sufficient condition for a regular function in the unit circle to be in the class \(\bar S^*(\alpha)\) or in the class \(B_ 1(\alpha)\) is proved.

Reviewer: S.Walczak

MSC:

30C45	Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C80	Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination

Keywords:

subordination