On Third-Order Differential Subordination and Superordination Properties of Analytic Functions Defined by a Generalized Operator

Symmetry

Sahsene Altınkaya¹  Waggas Galib Atshan²  Rajaa Ali Hiress³ 

[1] Department of Mathematics, Beykent University, 34500 Istanbul, Turkey;Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah 58001, Iraq;Education of Al-Qadisiyah, Ministry of Education, Diwaniyah 58001, Iraq;

关键词: analytic function;    subordination;    superordination;    sandwich result;    dominant;    subordinant;   

DOI  :  10.3390/sym14020418

来源: DOAJ

【 摘 要 】

In this current study, we aim to give some results for third-order differential subordination and superordination for analytic functions in $U=\left\{z\in ℂ:\left|z\right|<1\right\}$involving the generalized operator $I_{\alpha ,\beta }^{j}f$. The results are derived by investigating relevant classes of admissible functions. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted. The properties and results of the differential subordination are symmetry to the properties of the differential superordination to form the sandwich theorems.

【 授权许可】

Unknown