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Coefficient conditions for starlike functions

Published online by Cambridge University Press:  18 May 2009

S. Ruscheweyh
S. Ruscheweyh
Affiliation:
Math. Instttut d. Univ., D-8700 Würzburg, F.R.G.
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Let {ak} be a sequence of non-negative real numbers satisfying a1 = l and

(1)

Brannan [1] proved that the function

(2)

is close-to-convex univalent in the unit disc D. The example

shows that the conclusion in Brannan's theorem is sharp in that sense that “close-to-convex” cannot be replaced by the stronger one: “starlike”. It is therefore of interest to see which additional condition can guarantee this stronger conclusion.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 141 - 142
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

1.Brannan, D. A., On univalent polynomials, Glasgow Math. J., 11 (1970), 102–107CrossRefGoogle Scholar
2.Vietoris, L., Über das Vorzeichen gewisser trigonometrischer Summen, Sitzungsber, Oest. Akad. Wiss., 167(1958), 125–135Google Scholar