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Zbl 0617.30008
Ruscheweyh, S.
Coefficient conditions for starlike functions.
(English)
[J] Glasg. Math. J. 29, 141-142 (1987). ISSN 0017-0895; ISSN 1469-509X/e

The author gives two criteria for a function $f(z)=z+a\sb 2z\sp 2+...$, analytic in $U=\{z:\vert z\vert <1\}$, to be starlike in $U$: $$(1)\quad a\sb k\ge 0,\quad (k+1)a\sb{k+1}\le ka\sb k,\quad and\quad (2k+1)a\sb{2k+1}\le (2k-1)a\sb{2k};$$ $$(2)\quad f'\text{ typically real in U, and Ref'>0 in } U.$$ Criterion (1) extends an earlier result of the reviewer [ibid. 11, 102-107 (1970; Zbl 0207.076)].
[D.A.Brannan]
MSC 2000:
*30C45 Special classes of univalent and multivalent functions

Keywords: starlike functions; typically real

Citations: Zbl 0207.076

Cited in: Zbl 0656.30005

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