Differential subordination and superordination of a $q$-derivative operator connected with the $q$-exponential function

Document Type : Research Paper


1 Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq

2 Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia


In this article, we define a $q$-derivative operator of univalent functions associated with the $q$-exponential function. Moreover, we introduce differential subordination and differential superordination for the subordination class defined by this operator. Sandwich-type theorems of several known results also are derived by applying these results.


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Volume 13, Issue 2
July 2022
Pages 2795-2806
  • Receive Date: 08 May 2022
  • Revise Date: 14 June 2022
  • Accept Date: 15 July 2022