Let f be analytic in the unit disk \({\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1 \}\), and \({{\mathcal {S}}}\) be the subclass of normalized univalent functions given by \(f(z)=z+\sum _{n=2}^{\infty }a_n z^n\) for \(z\in {\mathbb {D}}\). We give sharp bounds for the modulus of the second Hankel determinant \( H_2(2)(f)=a_2a_4-a_3^2\) for the subclass \( {\mathcal F_{O}}(\lambda ,\beta )\) of strongly Ozaki close-to-convex functions, where \(1/2\le \lambda \le 1\), and \(0<\beta \le 1\). Sharp bounds are also given for \(|H_2(2)(f^{-1})|\), where \(f^{-1}\) is the inverse function of f. The results settle an invariance property of \(|H_2(2)(f)|\) and \(|H_2(2)(f^{-1})|\) for strongly convex functions.

令f在单位磁盘\（{\ mathbb {D}} = \ {z \ in {\ mathbb {C}}：| z | <1 \} \）中进行解析，而\（{{\ mathcal {S }}} \）是\（f（z）= z + \ sum _ {n = 2} ^ {\ infty} a_n z ^ n \）对于\（z \ in {\ mathbb {D}} \）。我们为子类\（{\ mathcal F_ {O}}（\ lambda，\ beta）\的第二个Hankel行列式\（H_2（2）（f）= a_2a_4-a_3 ^ 2 \）的模数给出了清晰的边界）的强Ozaki接近凸函数，其中\（1/2 \ le \ lambda \ le 1 \）和\（0 <\ beta \ le 1 \）。还为\（| H_2（2）（f ^ {-1}）| \）给出了锐界，其中\（f ^ {-1} \）是f的反函数。结果确定了强凸函数的不变性\（| H_2（2）（f）| \）和\（| H_2（2）（f ^ {-1}）| \）。