New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-Convex Functions Associated with the Cardioid Domain
In this paper, we define a new family of <i>q</i>-starlike and <i>q</i>-convex functions related to the cardioid domain utilizing the ideas of subordination and the Sălăgean quantum differential operator. The primary contribution of this article is the derivation of a sharp i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/6/1185 |
| _version_ | 1797592596675035136 |
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| author | Suha B. Al-Shaikh |
| author_facet | Suha B. Al-Shaikh |
| author_sort | Suha B. Al-Shaikh |
| collection | DOAJ |
| description | In this paper, we define a new family of <i>q</i>-starlike and <i>q</i>-convex functions related to the cardioid domain utilizing the ideas of subordination and the Sălăgean quantum differential operator. The primary contribution of this article is the derivation of a sharp inequality for the newly established subclasses of <i>q</i>-starlike and <i>q</i>-convex functions in the open unit disc <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">U</mi></semantics></math></inline-formula>. For this novel family, bounds of the first two Taylor-Maclaurin coefficients, the Fekete-Szegö-type functional, and coefficient inequalities are studied. Furthermore, we also investigate some new results for the inverse function belonging to the classes of <i>q</i>-starlike and <i>q</i>-convex functions. The results presented in this article are sharp. To draw connections between the early and present findings, several well-known corollaries are also highlighted. Symmetric quantum calculus operator theory can be used to investigate the symmetry properties of this new family of functions. |
| first_indexed | 2024-03-11T01:53:27Z |
| format | Article |
| id | doaj.art-c874933682494d14bd03dcbaf8943d19 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T01:53:27Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c874933682494d14bd03dcbaf8943d192023-11-18T12:50:39ZengMDPI AGSymmetry2073-89942023-06-01156118510.3390/sym15061185New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-Convex Functions Associated with the Cardioid DomainSuha B. Al-Shaikh0Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi ArabiaIn this paper, we define a new family of <i>q</i>-starlike and <i>q</i>-convex functions related to the cardioid domain utilizing the ideas of subordination and the Sălăgean quantum differential operator. The primary contribution of this article is the derivation of a sharp inequality for the newly established subclasses of <i>q</i>-starlike and <i>q</i>-convex functions in the open unit disc <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">U</mi></semantics></math></inline-formula>. For this novel family, bounds of the first two Taylor-Maclaurin coefficients, the Fekete-Szegö-type functional, and coefficient inequalities are studied. Furthermore, we also investigate some new results for the inverse function belonging to the classes of <i>q</i>-starlike and <i>q</i>-convex functions. The results presented in this article are sharp. To draw connections between the early and present findings, several well-known corollaries are also highlighted. Symmetric quantum calculus operator theory can be used to investigate the symmetry properties of this new family of functions.https://www.mdpi.com/2073-8994/15/6/1185analytic functionsunivalent functionsquantum-calculus<i>q</i>-convex and <i>q</i>-starlike functionssubordinationSălăgean <i>q</i>-differential operator shell-like curve |
| spellingShingle | Suha B. Al-Shaikh New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-Convex Functions Associated with the Cardioid Domain Symmetry analytic functions univalent functions quantum-calculus <i>q</i>-convex and <i>q</i>-starlike functions subordination Sălăgean <i>q</i>-differential operator shell-like curve |
| title | New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-Convex Functions Associated with the Cardioid Domain |
| title_full | New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-Convex Functions Associated with the Cardioid Domain |
| title_fullStr | New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-Convex Functions Associated with the Cardioid Domain |
| title_full_unstemmed | New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-Convex Functions Associated with the Cardioid Domain |
| title_short | New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of <i>q</i>-Starlike and <i>q</i>-Convex Functions Associated with the Cardioid Domain |
| title_sort | new applications of the salagean quantum differential operator for new subclasses of i q i starlike and i q i convex functions associated with the cardioid domain |
| topic | analytic functions univalent functions quantum-calculus <i>q</i>-convex and <i>q</i>-starlike functions subordination Sălăgean <i>q</i>-differential operator shell-like curve |
| url | https://www.mdpi.com/2073-8994/15/6/1185 |
| work_keys_str_mv | AT suhabalshaikh newapplicationsofthesalageanquantumdifferentialoperatorfornewsubclassesofiqistarlikeandiqiconvexfunctionsassociatedwiththecardioiddomain |