By making use of the concept of basic (or q-) calculus, a subclass ${\mathcal{S}}^{⁎}(\mathcal{L},q)$ of q-starlike functions, which is associated with the q-exponential function, is introduced here in the open unit disk $\mathbb{U}$ given by$\mathbb{U}=\{z:z\in \mathbb{C}\text{and}\left|z\right|<1\}.$ The main object of this article is to determine the upper bound of the third-order Hankel determinant $H_3(1)$ for functions belonging to the q-starlike function class ${\mathcal{S}}^{⁎}(\mathcal{L},q)$. For validity of our results, relevant connections with those in earlier works are also pointed out.

中文翻译：

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关于与q指数函数相关的q星形函数的子类的第三个Hankel行列式的上限

通过利用基本（或q-）演算的概念，一个子类${\mathcal{小号}}^{⁎}（\mathcal{大号}，q）$与q指数函数相关联的q -starlike函数的集合在此处引入开放式单元磁盘$\mathbb{ü}$ 由$\mathbb{ü}=\{ž：ž\in \mathbb{C}\text{和}\left|ž\right|<\mathrm{1个}\}。$ 本文的主要目的是确定三阶Hankel行列式的上限 $H_3（\mathrm{1个}）$用于属于q -starlike函数类的函数${\mathcal{小号}}^{⁎}（\mathcal{大号}，q）$。为了保证我们的结果的正确性，还指出了与早期作品中相关的联系。