Hankel and symmetric Toeplitz determinants for Sakaguchi starlike functions

Sushil Kumar, Swati Anand, Naveen Kumar Jain

Abstract


In this paper, we consider the class of starlike functions with respect to symmetric points which are also known as Sakaguchi starlike functions. We determine best possible bounds on Zalcman conjecture
$\vert a_n^2-a_{2n-1}\vert$ and generalized Zalcman conjecture $\vert a_ma_n-a_{m+n-1}\vert$ for $n=2$ and $n=4$, $m=2$, respectively for such functions. Further, we compute estimate on third order and fourth order Hankel determinants. As well, we also obtain estimates on third and fourth symmetric Toeplitz determinants.


Keywords


Starlike function; Sakaguchi starlike functions; Zalcman conjecture; third and forth order Hankel determinants; second, third and fourth order symmetric Toeplitz determinants.

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2024.3.04

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