Coefficient inequality for multivalent bounded turning functions of order $\alpha$

The objective of this paper is to obtain the sharp upper bound to the $H_{2}(p+1)$, second Hankel determinant for $p$-valent (multivalent) analytic bounded turning functions (also called functions whose derivatives have positive real parts) of order $\alpha~ (0\leq\alpha<1)$, using Toeplitz determinants. The result presented here includes three known results as their special cases.