Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. It is proved that the new operators preserve certain classes of univalent functions, such as classes of starlike and convex functions, and that they extend starlikeness of order \(\frac{1}{2}\) and convexity of order \(\frac{1}{2}\) to starlikeness and convexity, respectively. For obtaining the original results, the method of admissible functions is used, and the results are also written as differential inequalities and interpreted using inclusion properties for certain subsets of the complex plane. The example provided shows an application of the original results.

本文使用经典的 Bernardi 和 Libera 积分算子以及汇合（或 Kummer）超几何函数定义了两个新的积分算子。证明了新算子保留了某些类单价函数，例如类星函数和凸函数类，并且它们扩展了阶\(\frac{1}{2}\)的星状和阶\(\frac {1}{2}\)分别为星状和凸度。为了获得原始结果，使用了可容许函数的方法，并且结果也被写成微分不等式，并使用复平面的某些子集的包含属性来解释。提供的示例显示了原始结果的应用。