The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function

ZHANG Haiyan; TANG Huo; MA Lina

doi:10.6054/j.jscnun.2021062

Journal of South China Normal University (Natural Science Edition) > 2021 > 53(4): 84-90. > DOI: 10.6054/j.jscnun.2021062

ZHANG Haiyan, TANG Huo, MA Lina. The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(4): 84-90. DOI: 10.6054/j.jscnun.2021062

Citation:

PDF (1045 KB)

The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function

School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China

More Information

Received Date: November 29, 2020
Available Online: September 02, 2021

Graphical Abstract

Abstract

Abstract

Let $\mathcal{A}$ be a family of analytic functions with are the form $f(z)=z+\sum\limits_{n=2}^{\infty} a_{n} z^{n}$ on the open unit disk D. A class of analytic functions S_e^* which are defined on the open unit cicle D and associated with exponential function is introduced, that is $S_{e}^{*}=\left\{f \mid \frac{z f^{\prime}(z)}{f(z)}\prec\mathrm{e}^{z} \quad(f \in \mathcal{A}, z \in D)\right\}.$ And the upper bound of the fourth-order Hankel determinant H₄(1) for this function class S_e^* associated with exponential function is given.
- analytic function,
- Hankel determinant,
- exponential function,
- upper bound

FullText(HTML)

References (28)

References

[1]	MA W C, MINDA D. A unified treatment of some special classes of univalent functions[C]//Proceedings of the International Conference on Complex Analysis at the Nankai Institute of Mathematics. Tianjin: [s. n. ], 1992: 157-169.
[2]	SOKÓȽ J, STANKIEWICZ J. Radius of convexity of some subclasses of strongly starlike functions[J]. Zeszyty Naukowe Politechniki Rzeszowskiej Matematyka, 1996, 19: 101-105. http://www.researchgate.net/profile/Janusz_Sokol/publication/267137022_Radius_of_convexity_of_some_subclasses_of_strongly_starlike_functions/links/54980b460cf2c5a7e3428aad.pdf
[3]	MENDIRATTA R, NAGPAL S, RAVICHANDRAN V. A subclass of starlike functions associated with left-half of the lemniscate of Bernoulli[J]. International Journal of Mathematics, 2014, 25(9): 1-17.
[4]	MENDIRATTA R, NAGPAL S, RAVICHANDRAN V. On a subclass of strongly starlike functions associated with exponential function[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38: 365-386. doi: 10.1007/s40840-014-0026-8
[5]	POMMERENKE C H. On the coeffcients and Hankel determinants of univalent functions[J]. Journal of London Mathematical Society, 1966, 41: 111-122.
[6]	FEKETE M, SZEGÖ G. Eine benberkung über ungerada schlichte funktionen[J]. Journal of the London Mathematical Society, 1933, 8(2): 85-89. doi: 10.1112/jlms/s1-8.2.85/abstract
[7]	KOEPF W. On the Fekete-Szegö problem for close-to-convex functions[J]. American Mathematical Society, 1987, 101: 89-95.
[8]	KOEPF W. On the Fekete-Szegö problem for close-to-convex functions Ⅱ[J]. Archiv Der Mathematik, 1987, 49: 420-433. doi: 10.1007/BF01194100
[9]	SRIVASTAVA H M, HUSSAIN S A, RAZA M, et al. The Fekete-Szegö functional for a subclass of analytic functions associated with quasi-subordination[J]. Carpathian Journal of Mathematics, 2018, 34(1): 103-113. doi: 10.37193/CJM.2018.01.11
[10]	SRIVASTAVA H M, MISHRA A K, DAS M K. The Fekete-Szegö problem for a subclass of close-to-convex functions[J]. Complex Variables, Theory and Application, 2001, 44(2): 145-163. doi: 10.1080/17476930108815351
[11]	TANG H, SRIVAATAVA H M, SIVASUBRAMANIAN S, et al. The Fekete-Szegö functional problems for some classes of m-fold symmetric bi-univalent functions[J]. Journal of Mathematical Inequalities, 2016, 10(4): 1063-1092.
[12]	ZHANG H Y, TANG H, NIU X M. Third-order Hankel determinant for certain class of analytic functions related with exponential function[J]. Symmetry, 2018, 10(10): 501-508. doi: 10.3390/sym10100501
[13]	SHI L, SRIVASTAVA H M, ARIF M, et al. An investigation of the third Hankel determinant problem for certain subfamilies of univalent functions involving the exponential function[J]. Symmetry, 2019, 11(5): 598-611. doi: 10.3390/sym11050598
[14]	ZAPRAWA P. Hankel determinants for univalent functions related to the exponential function[J]. Symmetry, 2019, 11(10): 1211-1220. doi: 10.3390/sym11101211
[15]	BABALOLA K O. On H₃(1) Hankel determinant for some classes of univalent functions[J]. Inequality Theory and Applications, 2010, 6: 1-7. http://arxiv.org/abs/0910.3779
[16]	BANSAL D. Upper bound of second Hankel determinant for a new class of analytic functions[J]. Applied Mathematics Letters, 2013, 26(1): 103-107. doi: 10.1016/j.aml.2012.04.002
[17]	BANSAL D, MAHARANA S, PRAJAPAT J K. Third order Hankel determinant for certain univalent functions[J]. Journal of Korean Mathematical Society, 2015, 52(6): 1139-1148. doi: 10.4134/JKMS.2015.52.6.1139
[18]	ÇAǦLAR M, DENİZ E, SRIVASTAVA H M. Second Hankel determinant for certain subclasses of bi-univalent functions[J]. Turkish Journal of Mathematics, 2017, 41: 694-706. doi: 10.3906/mat-1602-25
[19]	JANTENG A, HALIM S A, DARUS M. Coefficient in-equality for a function whose derivative has a positive real part[J]. Journal of Inequalities in Pure and Applied, 2006, 7(2): 50/1-5.
[20]	JANTENG A, HALIM S A, DARUS M. Hankel determinant for starlike and convex functions[J]. International Journal of Mathematics Analysis, 2007, 13(1): 619-625.
[21]	LEE S K, RAVICHANDRAN V, SUBRAMANIAM S. Bou-nds for the second Hankel determinant of certain univalent functions[J]. Journal of Inequalities and Applications, 2013, 2013(281): 1-17.
[22]	RAZA M, MALIK S N. Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of bernoulli[J]. Journal of Inequalities and Applications, 2013, 2013(412): 1-8.
[23]	SRIVASTAVA H M, ALTINKAYA S, YALCIN S. Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator[J]. Filomat, 2018, 32(2): 503-516. doi: 10.2298/FIL1802503S
[24]	张海燕, 汤获, 马丽娜. 一类解析函数的三阶Hankel行列式的上界估计[J]. 纯粹数学与应用数学, 2017, 33(2): 211-220. doi: 10.3969/j.issn.1008-5513.2017.02.013 ZHANG H Y, TANG H, MA L N. Upper bound of third Hankel determinant for a class of analytic functions[J]. Pure and Applied Mathematics, 2017, 33(2): 211-220. doi: 10.3969/j.issn.1008-5513.2017.02.013
[25]	DUREN P L. Harmonic mappings in plane[M]. New York: Cambridge University Press, 2004.
[26]	LIBERA R J, ZLOTKIEWICZ E J. Coefficient bounds for the inverse of a function with derivative in P[J]. Proceedings of the American Mathematica, 1983, 87(2): 251-257.
[27]	RAVICHNDRAN V, VERMA S. Bound for the fifth coeffcient of certain starlike functions[J]. Comptes Rendus Mathematique, 2015, 353(6): 505-510. doi: 10.1016/j.crma.2015.03.003
[28]	POMMERENKE C. Univalent functions[M]. Providence: American Mathematical Society, 1975.

Cited By

Cited by

Periodical cited type(16)

1.	方斌，邵羽凡，孙新松，王子源，杨欣蕾. 粮食主产区农田食物供给服务与景观格局空间协调性研究——以江苏省连云港市为例. 长江流域资源与环境. 2025(03): 668-681 .
2.	王婷，顾嘉楠，张春英. 基于CNKI文献计量分析的近二十年国内景观格局演变研究. 福建建筑. 2025(02): 20-25 .
3.	张亚丽，陈亮，田义超，林俊良，黄柱军，杨芸珍，张强，陶进. 模拟多情景下桂西南峰丛洼地流域土地利用变化及生态系统服务价值的空间响应. 环境科学. 2024(12): 6935-6948 .
4.	郭健斌，刘天平. 基于土地利用的尼洋河流域生态系统服务价值的时空变化及其驱动因素. 华南师范大学学报(自然科学版). 2024(05): 64-76 .
5.	谢卓洪，刘利杰，莫燕卿，陈楚民，马振环，刘萍. 珠三角森林城市群区域性河流水系森林景观格局评价与优化. 林业资源管理. 2023(02): 118-125 .
6.	文嫱，徐颂军，邱彭华，钟尊倩. 城镇化背景下海口湿地近30年变化分析. 华南师范大学学报(自然科学版). 2023(03): 74-86 .
7.	罗继文，周禧，黄亚南，刘叶，张争胜，曾丽璇. 南沙区土地利用变化对生态系统服务价值的影响. 华南师范大学学报(自然科学版). 2022(03): 100-110 .
8.	魏嘉馨，干晓宇，黄莹，郭仲薇. 成都市城市绿地景观与生态系统服务的关系. 西北林学院学报. 2022(06): 232-241 .
9.	田翠翠，朱忆秋，褚艳玲，徐婷婷，陈龙. 粤港澳大湾区景观格局时空变化及其驱动力研究. 环境科学与管理. 2021(04): 98-103 .
10.	唐明坤，许戈，冯涌，刘亮，周大松，陈治兴，杨静，王恋，王新. 四川岷山山系大熊猫栖息地景观格局特征及保护策略研究. 四川林业科技. 2021(04): 5-11 .
11.	王小军，张楚然，廖倚凌，刘光旭，王炳香，余剑. 1980-2018年粤港澳大湾区人为干扰度的时空特征. 水土保持通报. 2021(03): 333-341 .
12.	纪树志. 极旱荒漠区湿地植被动态变化监测——以甘肃敦煌阳关国家级自然保护区为例. 中国农学通报. 2021(26): 105-109 .
13.	张洪，方文杰，陶柳延. 长三角中心城市社会经济-生态环境-旅游产业协调发展时空演化及影响因素——基于面板数据的空间计量分析. 华南师范大学学报(自然科学版). 2021(05): 84-91 .
14.	柳迪子，杜守帅，王晨旭. 旅游型乡村景观格局变化及生态系统服务价值响应——以江苏省无锡市太湖国家旅游度假区为例. 水土保持通报. 2021(05): 264-275+286 .
15.	胡喻璇，陈德超，范金鼎，施祝凯. 环太湖区域景观格局演变及其生态系统服务影响. 城市问题. 2021(04): 95-103 .
16.	吴健生，易腾云，王晗. 2000—2030年深港景观格局演变时空分异与趋势对比分析. 生态学报. 2021(22): 8718-8731 .

Other cited types(15)

Get Citation

PDF

XML

Article views (476) PDF downloads (63) Cited by(31)

Turn off MathJax

Article Contents

Abstract

References

The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function

Abstract

References

Cited by

Periodical cited type(16)

Other cited types(15)

Catalog

Export File

Citation

Format

Content