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SECOND HANKEL DETERMINANT FOR LOGARITHMIC INVERSE COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS
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- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 18 April 2024, pp. 1-12
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SECOND HANKEL DETERMINANT OF LOGARITHMIC COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 105 / Issue 3 / June 2022
- Published online by Cambridge University Press:
- 30 September 2021, pp. 458-467
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- June 2022
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LOGARITHMIC COEFFICIENTS OF SOME CLOSE-TO-CONVEX FUNCTIONS
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 2 / April 2017
- Published online by Cambridge University Press:
- 02 November 2016, pp. 228-237
- Print publication:
- April 2017
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The logarithmic coefficients
$\unicode[STIX]{x1D6FE}_{n}$ of an analytic and univalent function 
$f$ in the unit disc 
$\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ with the normalisation 
$f(0)=0=f^{\prime }(0)-1$ are defined by 
$\log (f(z)/z)=2\sum _{n=1}^{\infty }\unicode[STIX]{x1D6FE}_{n}z^{n}$. In the present paper, we consider close-to-convex functions (with argument 0) with respect to odd starlike functions and determine the sharp upper bound of 
$|\unicode[STIX]{x1D6FE}_{n}|$, 
$n=1,2,3$, for such functions 
$f$.
