This article deals with the -differential subordinations for starlike functions associated with the lemniscate of Bernoulli and cardioid domain. The primary goal of this work is to find the conditions on for , where is analytic function and is subordinated by the function which is producing cardioid domain as its image domain while mapping the open unit disk. Along with this, certain sufficient conditions for -starlikeness of analytic functions are determined.

中文翻译：

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心型相关星状功能的充裕度标准

本文讨论了与伯努利和心型指向子相关的星形函数的-微分从属。这项工作的主要目标是为，其中是解析函数，并且在映射打开的单元盘时会产生心形结构域作为其图像域，该函数从属于该函数。与此相伴，对于某些充分条件-的解析函数星形性被确定。