The main aim of the present article is the introduction of a new differential operator in -analogue for meromorphic multivalent functions which are analytic in punctured open unit disc. A subclass of meromorphic multivalent convex functions is defined using this new differential operator in -analogue. Furthermore, we discuss a number of useful geometric properties for the functions belonging to this class such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity. Also, algebraic property of closure is discussed of functions belonging to this class. Integral representation problem is also proved for these functions.

中文翻译：

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一个新的差分算子在Janowski型亚纯凸函数中的应用

本制品的主要目的是在引入新的微分算子-类似物亚纯函数的多价它们在刺破打开单元盘解析。的亚纯多凸函数的子类是使用这种新的微分算子定义-类似物。此外，我们讨论了属于该类的函数的许多有用的几何属性，例如充分性标准，系数估计，变形定理，增长定理，星形半径和凸半径。此外，讨论了属于此类的函数的闭包的代数性质。这些功能也证明了积分表示问题。