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© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

The theory of univalent functions has shown strong significance in the field of mathematics. It is such a vast and fully applied topic that its applications exist in nearly every field of applied sciences such as nonlinear integrable system theory, fluid dynamics, modern mathematical physics, the theory of partial differential equations, engineering, and electronics. In our present investigation, two subfamilies of starlike and bounded turning functions associated with a three-leaf-shaped domain were considered. These classes are denoted by BT3l and S3l*, respectively. For the class BT3l, we study various coefficient type problems such as the first four initial coefficients, the Fekete–Szegö and Zalcman type inequalities and the third-order Hankel determinant. Furthermore, the existing third-order Hankel determinant bounds for the second class will be improved here. All the results that we are going to prove are sharp.

Details

Title
The Sharp Bounds of Hankel Determinants for the Families of Three-Leaf-Type Analytic Functions
Author
Arif, Muhammad 1   VIAFID ORCID Logo  ; Omar Mohammed Barukab 2   VIAFID ORCID Logo  ; Sher Afzal Khan 1 ; Abbas, Muhammad 1 

 Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan; [email protected] (S.A.K.); [email protected] (M.A.) 
 Faculty of Computing and Information Technology, King Abdulaziz University, P.O. Box 411, Jeddah 21911, Saudi Arabia; [email protected] 
First page
291
Publication year
2022
Publication date
2022
Publisher
MDPI AG
e-ISSN
25043110
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2679715810
Copyright
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.