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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Main Authors: Qiuxia Hu, Rizwan Salim Badar, Muhammad Ghaffar Khan
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/13/12/842
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author Qiuxia Hu
Rizwan Salim Badar
Muhammad Ghaffar Khan
author_facet Qiuxia Hu
Rizwan Salim Badar
Muhammad Ghaffar Khan
author_sort Qiuxia Hu
collection DOAJ
description 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.
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spelling doaj-art-598127987a4b4f8e9dd4e14762c68a6d2025-08-20T02:55:42ZengMDPI AGAxioms2075-16802024-11-01131284210.3390/axioms13120842Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer OperatorQiuxia Hu0Rizwan Salim Badar1Muhammad Ghaffar Khan2Department of Mathematics, Luoyang Normal University, Luoyang 471934, ChinaDepartment of Mathematics, Allama Iqbal Open University, Islamabad 44000, PakistanInstitute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, PakistanThis 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.https://www.mdpi.com/2075-1680/13/12/842analytic functionconic domainquantum calculusq-Carlson–Shaffer operator
spellingShingle Qiuxia Hu
Rizwan Salim Badar
Muhammad Ghaffar Khan
Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer Operator
Axioms
analytic function
conic domain
quantum calculus
q-Carlson–Shaffer operator
title Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer Operator
title_full Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer Operator
title_fullStr Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer Operator
title_full_unstemmed Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer Operator
title_short Subclasses of <i>q</i>-Uniformly Starlike Functions Obtained via the <i>q</i>-Carlson–Shaffer Operator
title_sort subclasses of i q i uniformly starlike functions obtained via the i q i carlson shaffer operator
topic analytic function
conic domain
quantum calculus
q-Carlson–Shaffer operator
url https://www.mdpi.com/2075-1680/13/12/842
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AT rizwansalimbadar subclassesofiqiuniformlystarlikefunctionsobtainedviatheiqicarlsonshafferoperator
AT muhammadghaffarkhan subclassesofiqiuniformlystarlikefunctionsobtainedviatheiqicarlsonshafferoperator