Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Function Theory (SPFT), are significant in developing and providing further new studies. In complex domain, the convolution tool is a salutary technique for systematic analytical characterization of geometric functions. The analytic functions in the punctured unit disk are the so-called meromorphic functions. In this present analysis, a new convolution complex operator defined on meromorphic functions related with the Hurwitz-Lerch Zeta type functions and Kummer functions is considered. Certain sufficient stipulations are stated for several formulas of this defining operator to attain subordination. Indeed, these outcomes are an extension of known outcomes of starlikeness, convexity, and close to convexity.

中文翻译：

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亚纯Kummer函数的从属性质与Hurwitz-Lerch Zeta函数相关

最近，由于特殊功能理论（SPFT）和运算符理论（OPT）在纯数学和应用数学学科中的大量应用，引起了很多关注。作为特殊功能理论（SPFT）的一部分，Hurwitz-Lerch Zeta类型的函数在开发和提供进一步的新研究方面具有重要意义。在复杂领域，卷积工具是一种对几何函数进行系统分析表征的有益技术。穿孔单元盘中的解析函数是所谓的亚纯函数。在本分析中，考虑了在与Hurwitz-Lerch Zeta类型函数和Kummer函数相关的亚纯函数上定义的新卷积复算符。对于此定义运算符的多个公式，为了达到从属状态，规定了某些足够的规定。确实，