Sharp Bounds on Hankel Determinant of <i>q</i>-Starlike and <i>q</i>-Convex Functions Subordinate to Secant Hyperbolic Functions
In the present paper, using the <i>q</i>-difference operator, we introduce two classes of <i>q</i>-starlike functions and <i>q</i>-convex functions subordinate to secant hyperbolic functions. As functions in these classes have unique characteristic of missing coef...
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2025-05-01
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| author | Lifen Zhang Zhigang Wang Lei Shi |
| author_facet | Lifen Zhang Zhigang Wang Lei Shi |
| author_sort | Lifen Zhang |
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| description | In the present paper, using the <i>q</i>-difference operator, we introduce two classes of <i>q</i>-starlike functions and <i>q</i>-convex functions subordinate to secant hyperbolic functions. As functions in these classes have unique characteristic of missing coefficients on the second term in their analytic expansions, we define a new functional to unify the Hankel determinants with entries of the original coefficients, inverse coefficients, logarithmic coefficients, and inverse logarithmic coefficients for these functions. We obtain the sharp bounds on the new functional for functions in the two classes, and as a consequence, the best results on Hankel determinant for the starlike and convex functions subordinate to secant hyperbolic functions are given. The outcomes include some existing findings as corollaries and may help to deepen the understanding the properties of <i>q</i>-analogue analytic functions. |
| format | Article |
| id | doaj-art-23a51496eb3c43b988e3a23e58d5384c |
| institution | Matheson Library |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | Fractal and Fractional |
| spelling | doaj-art-23a51496eb3c43b988e3a23e58d5384c2025-06-25T13:51:51ZengMDPI AGFractal and Fractional2504-31102025-05-019634610.3390/fractalfract9060346Sharp Bounds on Hankel Determinant of <i>q</i>-Starlike and <i>q</i>-Convex Functions Subordinate to Secant Hyperbolic FunctionsLifen Zhang0Zhigang Wang1Lei Shi2School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, ChinaSchool of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, ChinaSchool of Mathematics and Statistics, Anyang Normal University, Anyang 455002, ChinaIn the present paper, using the <i>q</i>-difference operator, we introduce two classes of <i>q</i>-starlike functions and <i>q</i>-convex functions subordinate to secant hyperbolic functions. As functions in these classes have unique characteristic of missing coefficients on the second term in their analytic expansions, we define a new functional to unify the Hankel determinants with entries of the original coefficients, inverse coefficients, logarithmic coefficients, and inverse logarithmic coefficients for these functions. We obtain the sharp bounds on the new functional for functions in the two classes, and as a consequence, the best results on Hankel determinant for the starlike and convex functions subordinate to secant hyperbolic functions are given. The outcomes include some existing findings as corollaries and may help to deepen the understanding the properties of <i>q</i>-analogue analytic functions.https://www.mdpi.com/2504-3110/9/6/346Hankel determinant<i>q</i>-starlike functions<i>q</i>-convex functionssecant hyperbolic functions |
| spellingShingle | Lifen Zhang Zhigang Wang Lei Shi Sharp Bounds on Hankel Determinant of <i>q</i>-Starlike and <i>q</i>-Convex Functions Subordinate to Secant Hyperbolic Functions Fractal and Fractional Hankel determinant <i>q</i>-starlike functions <i>q</i>-convex functions secant hyperbolic functions |
| title | Sharp Bounds on Hankel Determinant of <i>q</i>-Starlike and <i>q</i>-Convex Functions Subordinate to Secant Hyperbolic Functions |
| title_full | Sharp Bounds on Hankel Determinant of <i>q</i>-Starlike and <i>q</i>-Convex Functions Subordinate to Secant Hyperbolic Functions |
| title_fullStr | Sharp Bounds on Hankel Determinant of <i>q</i>-Starlike and <i>q</i>-Convex Functions Subordinate to Secant Hyperbolic Functions |
| title_full_unstemmed | Sharp Bounds on Hankel Determinant of <i>q</i>-Starlike and <i>q</i>-Convex Functions Subordinate to Secant Hyperbolic Functions |
| title_short | Sharp Bounds on Hankel Determinant of <i>q</i>-Starlike and <i>q</i>-Convex Functions Subordinate to Secant Hyperbolic Functions |
| title_sort | sharp bounds on hankel determinant of i q i starlike and i q i convex functions subordinate to secant hyperbolic functions |
| topic | Hankel determinant <i>q</i>-starlike functions <i>q</i>-convex functions secant hyperbolic functions |
| url | https://www.mdpi.com/2504-3110/9/6/346 |
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