Present study on fourth order differential subordination associated with differential operator

Al-Mayyahi, Suad Y.; Jassim, Kassim A.

doi:10.47974/JIM-2086

Open Access Research Article

Present study on fourth order differential subordination associated with differential operator

^*Suad Y. Al-MayyahiCorresponding authorsyounis@uowasit.edu.iqDepartment of Mathematics College of Education of Pure Science University of Wasit Wasit, IraqView full profile → , Kassim A. Jassimkassim.jassim@sc.uobaghdad.edu.iqDepartment of Mathematics College of Science University of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1097–1108Vol. 28Issue 3-BApril 2025DOI: 10.47974/JIM-2086XML

Received:: 08 Oct 2024
Published Online:: 08 May 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2086
Pages:: 1097–1108

Abstract

Univalent functions represent a crucial area in complicated analysis applicable to both single and many variables. Researchers have performed a traditional analysis of this subject since at least 1907. Geometric function theory is synthesis for geometry & analysis. Various research has examined first-order differential subordination, subsequently leading to inquiries into second-order differential subordination within the unit disc. Abdulhalim and Miller [3] presented third-order differential subordination by reinterpreting essential inequalities of realvalued function inside framework ofor complexvalued function. This research seeks to formulate fourth-order differential subordination & superordination by application for generalized derivative operator Dγ,σs,m,k f(z) such that numerous theorems are stated and proved involving the generalized derivative operator Dγ,σs,m,k f(z) for analytic function [1] in open-unit disc A, which using generalised Srivastava-Attiya operator, generalised Al-Oboudi operator, binomial series. Based on this new operator, we derive results regarding fourth differential subordination and superordination technique for analytic functions related to operator Dγ,σs,m,k f(z) within the open unit disk A and we discuss these insights by examining relevant categories of admissible functions, some theories and colleries.

Keywords

Univalent functions Differential operator Admissible functions Univalent function Convolution

Subject Classifications

Primary 30C45Secondary 3080

References

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