On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (<i>p</i>,<i>q</i>)-Derivative Operator

On the Third Hankel Determinant of a Certain Subclass of Bi-Univalent Functions Defined by (<i>p</i>,<i>q</i>)-Derivative Operator

In this study, the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><...

Full description

Saved in:
Bibliographic Details
Main Authors: Mohammad El-Ityan, Qasim Ali Shakir, Tariq Al-Hawary, Rafid Buti, Daniel Breaz, Luminita-Ioana Cotîrlă
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
Subjects:
(<i>p</i>,<i>q</i>)-derivative operator
Fekete–Szegö
Hankel determinants
univalent
bi-univalent functions
Online Access:https://www.mdpi.com/2227-7390/13/8/1269
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this study, the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-derivative operator is used to define a novel class of bi-univalent functions. For this class, we define constraints on the coefficients up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo></mrow><msub><mo>ℓ</mo><mn>5</mn></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula>. The functions are analyzed using a suitable operational method, which enables us to derive new bounds for the Fekete–Szegö functional, as well as explicit estimates for important coefficients like <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo></mrow><msub><mo>ℓ</mo><mn>2</mn></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo></mrow><msub><mo>ℓ</mo><mn>3</mn></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula>. In addition, we establish the upper bounds of the second and third Hankel determinants, providing insights into the geometrical and analytical properties of this class of functions.
ISSN:2227-7390

Similar Items