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

Sokół J., İlhan S., Güney H. Ö.

Journal of Mathematics and Applications

2018

Vol. 41

195--206

We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shell-like 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.