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COEFFICIENT ESTIMATES FOR SOME CLASSES OF FUNCTIONS ASSOCIATED WITH
$q$-FUNCTION THEORY
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 3 / June 2017
- Published online by Cambridge University Press:
- 06 March 2017, pp. 446-456
- Print publication:
- June 2017
-
- Article
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- You have access
- Export citation
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For every
$q\in (0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach problem for the class of 
$q$-convex functions of order 
$\unicode[STIX]{x1D6FC}$ with 
$0\leq \unicode[STIX]{x1D6FC}<1$. In addition, we consider the Fekete–Szegö problem and the Hankel determinant problem for the class of 
$q$-starlike functions, leading to two conjectures for the class of 
$q$-starlike functions of order 
$\unicode[STIX]{x1D6FC}$ with 
$0\leq \unicode[STIX]{x1D6FC}<1$.
