In this paper we introduce some new subclasses of the p -valent analytic functions with higher-order derivatives that generalize some related subclasses of starlike and convex functions of a positive order. We found the order of ( p , q )-valent starlikeness and convexity for the products of functions that belong to these classes. The order of ( p , q )-valent starlikeness and convexity of certain integral operators for the product of functions of these classes were also obtained.

中文翻译：

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某些多价函数与高阶导数的乘积的星形和凸性

在本文中，我们介绍了带有高阶导数的p-价分析函数的一些新子类，这些子类概括了正序星形和凸函数的一些相关子类。我们发现属于这些类别的函数的乘积的（p，q）价星形和凸度的顺序。对于这些类的函数的乘积，还获得了某些积分算子的（p，q）价星形和凸度的顺序。