Starlike and Convex Functions Associated with a Nephroid Domain

被引:69
作者
Wani, Lateef Ahmad [1 ]
Swaminathan, A. [1 ]
机构
[1] Indian Inst Technol, Dept Math, Roorkee 247667, Uttarakhand, India
关键词
Starlike and convex functions; Subordination; Fekete-Szego problem; Cardioid; Nephroid; Lemniscate of Bernoulli; DIFFERENTIAL SUBORDINATION; LEMNISCATE; SUBCLASS;
D O I
10.1007/s40840-020-00935-6
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we show that the Caratheodory function phi Ne(z)=1+z-z3/3 onto the interior of the nephroid, a 2-cusped kidney-shaped curve, and introduce new Ma-Minda-type function classes SNeand CNeassociated with it. Apart from studying the characteristic properties of the region bounded by this nephroid, the structural formulas, extremal functions, growth and distortion results, inclusion results, coefficient bounds and Fekete-Szego problems are discussed for the classes SNe* and CNe. Moreover, for beta is an element of R and some analytic function p(z) satisfying p(0)=1, we prove certain subordination implications of the first-order differential subordination 1+beta zp '(z)/pj(z)& x227a;phi Ne(z),j=0,1,2, and obtain sufficient conditions for some geometrically defined function classes available in the literature.
引用
收藏
页码:79 / 104
页数:26
相关论文
共 35 条
[1]   Applications of first order differential subordination for functions with positive real part [J].
Ahuja, Om P. ;
Kumar, Sushil ;
Ravichandran, V .
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2018, 63 (03) :303-311
[2]  
Ali R.M., 2007, INT J MATH MATH SCI, P7
[3]   Coefficient bounds for p-valent functions [J].
Ali, Rosihan M. ;
Ravichandran, V. ;
Seenivasagan, N. .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 187 (01) :35-46
[4]   DIFFERENTIAL SUBORDINATION FOR FUNCTIONS ASSOCIATED WITH THE LEMNISCATE OF BERNOULLI [J].
Ali, Rosihan M. ;
Cho, Nak Eun ;
Ravichandran, V. ;
Kumar, S. Sivaprasad .
TAIWANESE JOURNAL OF MATHEMATICS, 2012, 16 (03) :1017-1026
[5]  
[Anonymous], 1991, Ann.Polon.math., DOI DOI 10.4064/ap-56-1-87-92
[6]   UNIVALENT POLYNOMIALS [J].
BRANNAN, DA .
GLASGOW MATHEMATICAL JOURNAL, 1970, 11 (JUL) :102-&
[7]   Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate [J].
Ch, Nak Eun ;
Kumar, Sushil ;
Kumar, Virendra ;
Ravichandran, V .
TURKISH JOURNAL OF MATHEMATICS, 2018, 42 (03) :1380-1399
[8]   Radius Problems for Starlike Functions Associated with the Sine Function [J].
Cho, N. E. ;
Kumar, V. ;
Kumar, S. S. ;
Ravichandran, V. .
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2019, 45 (01) :213-232
[9]  
Gandhi S, 2017, ASIAN-EUR J MATH, V10, DOI 10.1142/S1793557117500644
[10]   Certain Class of Starlike Functions Associated with Modified Sigmoid Function [J].
Goel, Priyanka ;
Kumar, S. Sivaprasad .
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (01) :957-991