Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer Operator

Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer Operator

This article investigates the applications of the <i>q</i>-Carlson–Shaffer operator on subclasses of q-uniformly starlike functions, introducing the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics>&l...

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Bibliographic Details
Main Authors: Qiuxia Hu, Rizwan Salim Badar, Muhammad Ghaffar Khan
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Axioms
Subjects:
analytic function
conic domain
quantum calculus
q-Carlson–Shaffer operator
Online Access:https://www.mdpi.com/2075-1680/13/12/842
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Summary:This article investigates the applications of the <i>q</i>-Carlson–Shaffer operator on subclasses of q-uniformly starlike functions, introducing the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>T</mi><mi>q</mi></msub><mrow><mo>(</mo><mi>m</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. The study establishes a necessary condition for membership in this class and examines its behavior within conic domains. The article delves into properties such as coefficient bounds, the Fekete–Szegö inequality, and criteria defined via the Hadamard product, providing both necessary and sufficient conditions for these properties.
ISSN:2075-1680

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