On third Hankel determinants for subclasses of analytic functions and close-to-convex harmonic mappings

被引:7
作者
Sun, Yong [1 ]
Wang, Zhi-Gang [2 ]
Rasila, Antti [3 ]
机构
[1] Hunan Inst Engn, Sch Sci, Xiangtan 411104, Hunan, Peoples R China
[2] Hunan First Normal Univ, Sch Math & Comp Sci, Changsha 410205, Hunan, Peoples R China
[3] Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland
来源
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2019年 / 48卷 / 06期
关键词
Univalent function; starlike function; convex function; bounded turning function; close-to-convex function; harmonic mapping; Hankel determinant; FEKETE-SZEGO PROBLEM; UNIVALENT; COEFFICIENTS; INVERSE;
D O I
10.15672/HJMS.2018.632
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we obtain the upper bounds to the third Hankel determinants for convex functions of order alpha and bounded turning functions of order alpha. Furthermore, several relevant results on a new subclass of close-to-convex harmonic mappings are obtained. Connections of the results presented here to those that can be found in the literature are also discussed.
引用
收藏
页码:1695 / 1705
页数:11
相关论文
共 40 条
[1]   Extremal problems on the class of convex functions of order-1/2 [J].
Abu Muhanna, Yusuf ;
Li, Liulan ;
Ponnusamy, Saminathan .
ARCHIV DER MATHEMATIK, 2014, 103 (06) :461-471
[2]  
[Anonymous], 2013, J. Inequalities Appl, DOI [DOI 10.1186/1029-242X-2013-412, 10.1186/1029-242X-2013-412]
[3]  
Babalola KO, 2010, INEQUAL THEORY APPL, P1
[4]   THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS [J].
Bansal, Deepak ;
Maharana, Sudhananda ;
Prajapat, Jugal Kishore .
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2015, 52 (06) :1139-1148
[5]   Upper bound of second Hankel determinant for a new class of analytic functions [J].
Bansal, Deepak .
APPLIED MATHEMATICS LETTERS, 2013, 26 (01) :103-107
[6]   COEFFICIENT CONDITIONS FOR HARMONIC UNIVALENT MAPPINGS AND HYPERGEOMETRIC MAPPINGS [J].
Bharanedhar, S. V. ;
Ponnusamy, S. .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2014, 44 (03) :753-777
[7]   On close-to-convex harmonic mappings [J].
Bshouty, D. ;
Joshi, S. S. ;
Joshi, S. B. .
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2013, 58 (09) :1195-1199
[8]   Close-to-Convexity Criteria for Planar Harmonic Mappings [J].
Bshouty, D. ;
Lyzzaik, A. .
COMPLEX ANALYSIS AND OPERATOR THEORY, 2011, 5 (03) :767-774
[9]   POWER SERIES WITH INTEGRAL COEFFICIENTS [J].
CANTOR, DG .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1963, 69 (03) :362-&
[10]   Coefficient estimates and radii problems for certain classes of polyharmonic mappings [J].
Chen, J. ;
Rasila, A. ;
Wang, X. .
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2015, 60 (03) :354-371