Applications of Differential Inequalities Employing A New ConvolutedOperator Constructed by The Supertrigonometric Function

Zainab E.  Abdulnaby; Rabha W.  Ibrahim

doi:10.24996/ijs.2024.65.6.29

Authors

Zainab E. Abdulnaby Department of Mathematics, College of Sciences, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0001-5545-6564
Rabha W. Ibrahim Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, PC: 99138, Nicosia /Mersin 10 – Turkey / Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon / Information and Communication Technology Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar, Iraq

DOI:

https://doi.org/10.24996/ijs.2024.65.6.29

Keywords:

Univalent functions, Hypergeometric supertrigonometric functions, Hadamard product, Differential Subordination, Differential superordination

Abstract

In order to examine various geometric features, we expanded the supertrigonometric function (STF) and superhyperbolic function (SHF) into the open unit disk. A convolution differential operator of the STF provides the formulas. The suggested operator works with both integral and double differential inequalities. As a result, we present a collection of findings that includes recent works. The idea of
subordination and superordination serves as a guide for our method, and we then developed the primary conclusion as a double side’s theorem.