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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2024-11-01
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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. |
| format | Article |
| id | doaj-art-598127987a4b4f8e9dd4e14762c68a6d |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| 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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