Year: 2024
Type: article
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 de- termine best possible bounds on Zalcman conjecture |a_n^2 – a_(2n-1) | 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. Keywords: Starlike function, Sakaguchi starlike functions, Zalcman conjecture, third and forth order Hankel determinants, second, third and fourth order symmetric Toeplitz determinants.
Authors: Sushil Kumar, Swati Anand, Naveen Kumar Jain
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403082670