4.7 Article

The Sharp Bounds of Hankel Determinants for the Families of Three-Leaf-Type Analytic Functions

期刊

FRACTAL AND FRACTIONAL
卷 6, 期 6, 页码 -

出版社

MDPI
DOI: 10.3390/fractalfract6060291

关键词

analytic (or holomorphic) functions; univalent functions; subordination principle; Schwarz function; coefficient bounds; Hankel determinant

资金

  1. Institutional Fund Projects [IFPIP: 369-830-1442]
  2. Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia

向作者/读者索取更多资源

The theory of univalent functions is highly significant in mathematics and has widespread applications. This study focuses on two subfamilies of functions associated with a three-leaf-shaped domain and investigates various coefficient type problems for these functions.
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 S-3l*, respectively. For the class BT3l, we study various coefficient type problems such as the first four initial coefficients, the Fekete-Szego 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.

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