Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid Functions
The study of the Hankel determinant generated by the Maclaurin series of holomorphic functions belonging to particular classes of normalized univalent functions is one of the most significant problems in geometric function theory. Our goal in this study is first to define a family of alpha-convex fu...
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MDPI AG
2024-12-01
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| author | Muhammad Abbas Reem K. Alhefthi Daniele Ritelli Muhammad Arif |
| author_facet | Muhammad Abbas Reem K. Alhefthi Daniele Ritelli Muhammad Arif |
| author_sort | Muhammad Abbas |
| collection | DOAJ |
| description | The study of the Hankel determinant generated by the Maclaurin series of holomorphic functions belonging to particular classes of normalized univalent functions is one of the most significant problems in geometric function theory. Our goal in this study is first to define a family of alpha-convex functions associated with modified sigmoid functions and then to investigate sharp bounds of initial coefficients, Fekete-Szegö inequality, and second-order Hankel determinants. Moreover, we also examine the logarithmic and inverse coefficients of functions within a defined family regarding recent issues. All of the estimations that were found are sharp. |
| format | Article |
| id | doaj-art-f24114424f0d4e57adf9b2db04f39b58 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-f24114424f0d4e57adf9b2db04f39b582024-12-27T14:10:22ZengMDPI AGAxioms2075-16802024-12-01131284410.3390/axioms13120844Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid FunctionsMuhammad Abbas0Reem K. Alhefthi1Daniele Ritelli2Muhammad Arif3Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, PakistanDepartment of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Statistical Sciences, Università di Bologna, 40126 Bologna, ItalyDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, PakistanThe study of the Hankel determinant generated by the Maclaurin series of holomorphic functions belonging to particular classes of normalized univalent functions is one of the most significant problems in geometric function theory. Our goal in this study is first to define a family of alpha-convex functions associated with modified sigmoid functions and then to investigate sharp bounds of initial coefficients, Fekete-Szegö inequality, and second-order Hankel determinants. Moreover, we also examine the logarithmic and inverse coefficients of functions within a defined family regarding recent issues. All of the estimations that were found are sharp.https://www.mdpi.com/2075-1680/13/12/844alpha-convex functionmodified sigmoid functionlogarithmic coefficientsinverse coefficientscoefficient boundsFekete-Szegö inequality |
| spellingShingle | Muhammad Abbas Reem K. Alhefthi Daniele Ritelli Muhammad Arif Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid Functions Axioms alpha-convex function modified sigmoid function logarithmic coefficients inverse coefficients coefficient bounds Fekete-Szegö inequality |
| title | Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid Functions |
| title_full | Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid Functions |
| title_fullStr | Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid Functions |
| title_full_unstemmed | Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid Functions |
| title_short | Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid Functions |
| title_sort | sharp second order hankel determinants bounds for alpha convex functions connected with modified sigmoid functions |
| topic | alpha-convex function modified sigmoid function logarithmic coefficients inverse coefficients coefficient bounds Fekete-Szegö inequality |
| url | https://www.mdpi.com/2075-1680/13/12/844 |
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