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On norm estimation for certain subclasses of analytic functions in geometric functions theory | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 247-254 اصل مقاله (477.38 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19449.1254 | ||
| نویسنده | ||
| Hormoz Rahmatan* | ||
| Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran | ||
| چکیده | ||
| We investigate on some subclasses of analytic fuctions defined by subordination. Also, we give estimates of $\sup_{|z|<1}\big(1-|z|^{2}\big)\big|\dfrac{f^{''}(z)}{f^{'}(z)}\big|$, for functions belonging to extended class of starlike functions. For a locally univalent analytic function $f$ defined on $\Delta =\{z\in \mathbb{C}: |Z|<1\}$, we consider the pre-Schwarzian norm by $\Vert T\Vert=\sup _{|z|<1}\big(1-|z|^{2}\big)\big|\dfrac{f^{''}(z)}{f^{'}(z)}\big|$. In this work, we find the sharp norm estimate for the functions $f$ in the extended classes of starlike functions. | ||
| کلیدواژه‌ها | ||
| Analytic Functions؛ Starlike functions؛ Pre-schwarzian derivatives؛ Subordination | ||
| مراجع | ||
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[7] Najafzadeh. Sh, Rahmatan. H, Haji. H, Application of subordination for estimating the Hankel determinant for subclass of univalent functions, Creat. Math. Inform, 30(2021), 69{74.
[8] Rana. S, Goswami. P, Dubey. R. S, The norm of pre-Schwarzian derivative on subclasses of bi-univalent functions, AIMS Mathematics, 3(4)(2018), 600{607
[9] Raina. R. K, Sokol. J, Some properties related to a certain class of starlike functions, C. R. Math. Acad. Sci. Paris 353 (2015), no. 11, 973{978.
[10] Rahmatan. H, Shokri. A, Ahmad. H, Botmart. T Subordination Method for the Estimation of Certain Subclass of Analytic Functions De ned by the q-Derivative Operator, Journal of Function Spaces, Volume 2022, Article ID 5078060, 9 pages
[11] Rahmatan. H, Haji. H, Najafzadeh. SH, Coecient estimates and Fekete-Szego coecient inequality for new subclasses of Bi-univalent functions, Caspian Journal of Mathematical Sciences, 10(1)(2021), 39{50.
[12] Rahmatan. H, Najafzadeh. SH, Haji. H, Initial coecient bounds for interesting subclasses of meromorphic and bi-univalent functions, J. Mahani Math. Res. Cent. 11(2)(2022), 9{17.
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