A note on a class of pp-valent starlike functions of order beta

In this paper we obtain sharp coefficient bounds for certain $p$-valent starlike functions of order $\beta$, $0\le \beta<1$. Initially this problem was handled by Aouf in "M. K. Aouf, On a class of $p$-valent starlike functions of order $\alpha$, Internat. J. Math. $\&$ Math. Sci. 1987;10:733--744". We pointed out that the proof given by Aouf was incorrect and a correct proof is presented in this paper.Comment: 6 pages, 1 table, submitted to a journa

Bounds for the Second Hankel Determinant of Certain Univalent Functions

The estimates for the second Hankel determinant a_2a_4-a_3^2 of analytic function f(z)=z+a_2 z^2+a_3 z^3+...b for which either zf'(z)/f(z) or 1+zf"(z)/f'(z) is subordinate to certain analytic function are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for the Hankel determinant of strongly starlike, parabolic starlike, lemniscate starlike functions are obtained