Hankel and symmetric Toeplitz determinants for Sakaguchi starlike functions
DOI:
https://doi.org/10.24193/subbmath.2024.3.04Keywords:
Starlike function, Sakaguchi starlike functions, Zalcman conjecture, third and forth order Hankel determinants, second, third and fourth order symmetric Toeplitz determinantsAbstract
In this paper, we consider the class of starlike functions with respect to symmetric points which are also known as Sakaguchi starlike functions. We de- termine best possible bounds on Zalcman conjecture | – and generalized Zalcman conjecture |aman − am+n−1| 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.
Mathematics Subject Classification (2010): 30C45, 30C80.
Received 08 April 2022; Accepted 23 June 2022.
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