پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 660 |
| تعداد مقالات | 9,661 |
| تعداد مشاهده مقاله | 68,762,133 |
| تعداد دریافت فایل اصل مقاله | 48,273,108 |
New subclass of analytic functions defined by subordination | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 68، دوره 12، شماره 1، مرداد 2021، صفحه 847-855 اصل مقاله (599.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2018.13582.1706 | ||
| نویسندگان | ||
| Hossein Naraghi؛ Parvaneh Najmadi* ؛ Bahman Taherkhani | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| تاریخ دریافت: 12 دی 1396، تاریخ بازنگری: 08 تیر 1397، تاریخ پذیرش: 08 تیر 1397 | ||
| چکیده | ||
| By using the subordination relation $"\prec"$, we introduce an interesting subclass of analytic functions as follows: \begin{equation*} \mathcal{S}^*_{\alpha}:=\left\{f\in \mathcal{A}:\frac{zf'(z)}{f(z)}\prec \frac{1}{(1-z)^\alpha},\ \ |z|<1\right\}, \end{equation*} where $0<\alpha\leq1$ and $\mathcal{A}$ denotes the class of analytic and normalized functions in the unit disk $|z|<1$. In the present paper, by the class $\mathcal{S}^*_{\alpha}$ and by the Nunokawa lemma we generalize a famous result connected to starlike functions of order $1/2$. Also, coefficients inequality and logarithmic coefficients inequality for functions of the class $\mathcal{S}^*_{\alpha}$ are obtained. | ||
| کلیدواژه‌ها | ||
| univalent؛ subordination؛ starlike functions؛ coefficients estimates؛ logarithmic coefficients؛ Nunokawa's lemma | ||
| مراجع | ||
|
[1] L. De Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985) 137–152. [2] O. Dvorak, On funkcich prosty, Casopis Pest. Mat. 63 (1934) 9–16. [3] W. Janowski, Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math. 23 (1971) 159–177. [4] R. Kargar, A. Ebadian and J. Sokol, On Booth lemniscate and starlike functions, Anal. Math. Phys. 9 (2019) 143–154. [5] R. Kargar, A. Ebadian and J. Sokol, Radius problems for some subclasses of analytic functions, Complex Anal. Oper. Theory 11 (2017) 1639–1649. [6] S. Kumar and V. Ravichandran, A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40 (2016) 199–212. [7] K. Kuroki and S. Owa, Notes on new class for certain analytic functions, RIMS Kokyuroku Kyoto Univ. 1772 (2011) 2125. [8] W. Ma and, D. Minda, A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis (Z. Li, F. Ren, L. Yang, and S. Zhang, eds.), International Press Inc., 1992, pp. 157–169. [9] W. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math. 57 (1992) 165–175. [10] R. Mendiratta, S. Nagpal and V. Ravichandran, A subclass of starlike functions associated with left–half of the lemniscate of Bernoulli, Int. J. Math. 25 (2014), 17 pp. [11] R. Mendiratta, S. Nagpal and V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc. 38 (2015) 365–386. [12] K. Noshiro, On the theory of schlicht functions, J. Fac. Sci. Hokkaido Univ. 2 (1934–35) 129–155. [13] M. Nunokawa, On properties of non-Caratheodory functions, Proc. Jpn. Acad., Ser. A, Math. Sci. 68 (1992) 152–153. [14] R.K. Raina and J. Sokol, Some properties related to a certain class of starlike functions, C. R. Math. Acad. Sci. Paris 353 (2015) 973–978. [15] M.I.S. Robertson, On the theory of univalent functions, Ann. Math. 37 (1936) 374–408. [16] M.S. Robertson, Certain classes of starlike functions, Michigan Math. J. 76 (1954) 755–758. [17] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc. 48 (1943) 48–82. [18] K. Sharma, N.K. Jain and V. Ravichandran, Starlike functions associated with a cardioid, Afr. Mat. 27 (2016) 923–939. [19] J. Sokol, A certain class of starlike functions, Comput. Math. Appl. 62 (2011) 611–619. [20] J. Sokol and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. 19 (1996) 101–105. [21] S. Warschawski, On the higher derivatives at the boundary in conformal mappings, Trans. Amer. Math. Soc. 38 (1935) 310–340. | ||
|
آمار تعداد مشاهده مقاله: 15,692 تعداد دریافت فایل اصل مقاله: 7,509 |
||