ESTIMATE OF HANKEL DETERMINANT BOUNDS FOR TH CLASS OF THREE-LEAF-TYPE BOUNDED TURNING FUNCTIONS DEFINED WITH SUBORDINATION

Résumé

motive of the present investigation is to study a generalized
subclass of bounded turning functions associated with three-leaf type function
in the open unit disc E = {z ∈ C : |z| < 1}. We focus on the computation
of sharp upper bounds of the first four coefficients, Fekete-Szeg¨o inequality,
second Hankel determinant, Zalcman inequality and third Hankel determinant,
for the class defined here. Furthermore, these results have also been studied
for two-fold and three-fold symmetric functions. Some earlier known results
follow as consequences of the results derived in this paper.