Third-Order Sandwich Results for Analytic Univalent Functions Involving a New Hadamard Product Operator

Qasim Ali  Shakir; Waggas Galib  Atshan

doi:10.24996/ijs.2025.66.7.17

Authors

Qasim Ali Shakir Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah- Iraq https://orcid.org/0009-0002-2734-9432
Waggas Galib Atshan Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah- Iraq

DOI:

https://doi.org/10.24996/ijs.2025.66.7.17

Keywords:

Differential subordination, Hadamard product, Superordination, Analytic function, Sandwich theorem, Third-order

Abstract

The objective of this paper is to examine the outcomes of third-order differential subordination and superordination for analytic functions within the region , specifically focusing on the utilization of the novel Hadamard operator . The results are derived by analyzing relevant categories of allowable functions. New findings have been found about differential subordination and superordination, along with the discovery of several sandwich theorems. Furthermore, other specific instances are also seen. The qualities and outcomes of differential subordination exhibit symmetry with the properties of differential superordination, leading to the formulation of the sandwich theorems.