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New results of modern concept on the fourth-Hankel determinant of a certain subclass of analytic functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، Special Issue، اسفند 2021، صفحه 2243-2255 اصل مقاله (405.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.6116 | ||
| نویسندگان | ||
| Sarab Dakhil Theyab* 1؛ Waggas Galib Atshan2؛ Habeeb Kareem Abdullah1 | ||
| 1Department of Mathematics, Faculty of Education for Girls, University of Kufa, Najaf, Iraq | ||
| 2Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah, Iraq | ||
| تاریخ دریافت: 23 مهر 1400، تاریخ بازنگری: 22 آبان 1400، تاریخ پذیرش: 17 آذر 1400 | ||
| چکیده | ||
| A form for the fourth Hankel determinant is given in this paper as $$H_4 (1)=\begin{vmatrix} 1 & \mathfrak{a}_2 & \mathfrak{a}_3 & \mathfrak{a}_4 \\ \mathfrak{a}_2 & \mathfrak{a}_3 & \mathfrak{a}_4 & \mathfrak{a}_5 \\ \mathfrak{a}_3 & \mathfrak{a}_4 & \mathfrak{a}_5 & \mathfrak{a}_6 \\ \mathfrak{a}_4 & \mathfrak{a}_5 & \mathfrak{a}_6 & \mathfrak{a}_7 \\ \end{vmatrix}$$ The modern concept of the fourth Hankel determinant is studied for the subclass of analytic functions $\mu \left(\beta ,\lambda ,t\right)$ defined here using the concept of subordination. Bounds on the coefficients $\left|a_n\right|$ with n = 2,3,4, 5,6,7 for the functions in this newly introduced class are given and the upper bound of the fourth Hankel determinant for this class is obtained. Lemmas used by the authors of this paper improve the results from a previously published paper. Interesting particular cases are given in the corollaries of the main theorems. | ||
| کلیدواژهها | ||
| Subordination؛ Analytic Function؛ Fourth Hankel Determinant؛ Coefficient Bounds | ||
| مراجع | ||
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