An upper bound for third Hankel determinant of starlike functions related to shell-like curves connected with Fibonacci numbers

We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shelllike curves and connected with Fibonacci numbers. For this, firstly, we prove a conjecture, posed in [17], for sharp upper bound of second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions. AMS Subject Classification: 30C45, 30C50.