Sharp bounds of third Hankel determinant for a class of starlike functions and a subclass of q-starlike functions

[摘要] Following the trend of coefficient bound problems in Geometric Function Theory, in the present paper, the authors obtain the sharp bound of third Hankel determinant for the classes $S^*$, of starlike functions and $SL^*_q$, of $q$-starlike functions related with lemniscate of Bernoulli. Bound on the functions in the initial class, apart from being sharp is also an improvement over the known existing bound and the bound on the latter class generalizes the prior known outcome. Further, the extremal functions of classes $S^*$ and $SL^*_q$ are deduced to prove the sharpness of these results.

[学科分类] 公共、环境与职业健康

[关键词] sharp bounds;third Hankel determinant;$q$-Starlike functions;Carath'{e}odory coefficients;lemniscate of Bernoulli