Subordination problems for certain meromorphic functions

Document Type : Original Article

Authors

H. Özlem Güney ¹

Shigeyoshi Owa ²

¹ Department of Mathematics, Faculty of Science, Dicle University, Diyarbakır, Turkey

² Honorary Professor, ``1 Decembrie 1918" University of Alba Iulia, 510009 Alba Iulia, Romania

10.22034/kjm.2023.393104.2841

Abstract

Let $\Sigma$ be the class of meromorphic functions $f(z)$ of the form $f(z)=\frac{1}{z}+a_0+a_1z+\cdots$ which are analytic in the punctured disk $\mathbb{U}_0.$ For $f(z)\in\Sigma,$ operators $D^n f(z)$ with $n\in \mathbb{Z}=\{\cdots,-1,0,1,\cdots\}$ are introduced. Applying differential subordinations for analytic functions in the open unit disc $\mathbb{U},$ some interesting properties of $f(z)\in\Sigma$ with $D^n f(z)$ are discussed and argument problems of $D^n f(z)$ are given. Also, we consider some simple problems for our results.

Keywords

Meromorphic function

analytic function

differential subordination

argument problem

Subjects

• 30 Functions of a complex variable

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