Sharp coefficient estimates for certain subclasses of starlike functions of complex order

2013 ◽  
Vol 225 ◽  
pp. 43-49 ◽  
Author(s):  
Qing-Hua Xu ◽  
Qiao-Min Cai ◽  
H.M. Srivastava
Keyword(s):  
Starlike Functions ◽  
Coefficient Estimates ◽  
Complex Order

scholarly journals Research on Geometric Mappings in Complex Systems Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Yanyan Cui ◽  
Chaojun Wang ◽  
Sifeng Zhu
Keyword(s):  
Banach Spaces ◽  
Systems Analysis ◽  
Starlike Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Reinhardt Domains ◽  
Complex Order ◽  
Starlike Mappings

We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order λ, in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order λ. By the properties of functions with positive real parts and considering the zero of order k, we obtain the coefficient estimates for almost starlike functions of complex order λ on D. We also discuss the invariance of almost starlike mappings of complex order λ on Reinhardt domains and on the unit ball B in complex Banach spaces. The conclusions contain and generalize some known results.

scholarly journals Coefficient estimates for certain subclasses of starlike functions of complex order associated with hyperbolic domain

2021 ◽  
Vol 13(62) (2) ◽  
pp. 595-610
Author(s):  
K.R. Karthikeyan ◽  
G. Murugusundaramoorthy ◽  
A. Nistor-Serban
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Complex Order ◽  
Coefficient Inequalities ◽  
Hyperbolic Domain

In this paper, we obtain the coefficient inequalities for functions in certain subclasses of Janowski starlike functions of complex order which are related starlike functions associated with a hyperbolic domain. Our results extend the study of various subclasses of analytic functions. Several applications of our results are also mentioned

scholarly journals Starlike functions of complex order involving q-hypergeometric functions with fixed point

2014 ◽  
Vol 13 (1) ◽  
pp. 51-63
Author(s):  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Murugesan Kasthuri
Keyword(s):  
Fixed Point ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Function Class ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Open Disc ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractRecently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).

scholarly journals COEFFICIENT ESTIMATES FOR BOUNDED STARLIKE FUNCTIONS OF COMPLEX ORDER

1994 ◽  
Vol 25 (2) ◽  
pp. 113-123
Author(s):  
M. K. AOUF
Keyword(s):  
Positive Integer ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Complex Order ◽  
Class Of Functions

Let $F(b,M,n)$($b\neq 0$, complex, $M >1/2$, and $n$ is a positive integer) denote the classof functions $f(z)=z+\sum_{k=n+1}^\infty a_kz^k$ analytic in $U=\{z: |z|< 1\}$ which satisfy for fixed $M$, $f (z)/z \neq 0$ in $U$ and  \[ \left|\frac{b-1+\frac{zf'(z)}{f(z)}}{b}-M\right|<M, \quad z\in U.\] Also let $F^*(b,M,n)$ ($b\neq 0$, complex, $M >1/2$, and $n$ is a positive integer) denote the class of functions $f(z)=1/z+\sum_{k=n}^\infty a_kz^k$ analytic in the annulus $U^* = \{z : 0 < |z| < 1\}$ which satisfy \[ \left|\frac{b-1+\frac{zf'(z)}{f(z)}}{b}-M\right|<M, \quad z\in U^*.\] In this paper we obtain bounds for the coefficients of functions of the above classes.

scholarly journals Coefficient estimates for certain subfamilies of close-to-convex functions of complex order

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1139-1142 ◽  
Author(s):  
Wasim Ul-Haq ◽  
Attiya Nazneen ◽  
Nasir Rehman
Keyword(s):  
Differential Equation ◽  
Recent Work ◽  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Coefficient Bounds ◽  
Homogeneous Differential Equation ◽  
Complex Order ◽  
Appl Math

Motivated from the recent work of Srivastava et al. (H.M. Srivastava, O. Alt?ntas?, S. K. Serenbay, Coefficient bounds for certain subclasses of starlike functions of complex order, Appl. Math. Lett. 24(2011)1359-1363.), we aim to determine the coefficient estimates for functions in certain subclasses of close-to-convex and related functions of complex order, which are here defined by means of Cauchy-Euler type non-homogeneous differential equation. Several interesting consequences of our results are also observed.

COEFFICIENT ESTIMATES FOR SOME CLASSES OF FUNCTIONS ASSOCIATED WITH -FUNCTION THEORY

2017 ◽  
Vol 95 (3) ◽  
pp. 446-456 ◽  
Author(s):  
SARITA AGRAWAL
Keyword(s):  
Convex Functions ◽  
Representation Theorem ◽  
Function Theory ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Coefficient Estimates

For every $q\in (0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach problem for the class of $q$-convex functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$. In addition, we consider the Fekete–Szegö problem and the Hankel determinant problem for the class of $q$-starlike functions, leading to two conjectures for the class of $q$-starlike functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$.

Coefficient bounds for a subclass of starlike functions of complex order

2011 ◽  
Vol 218 (3) ◽  
pp. 693-698
Author(s):  
Murat Çağlar ◽  
Erhan Deniz ◽  
Halit Orhan
Keyword(s):  
Starlike Functions ◽  
Coefficient Bounds ◽  
Complex Order

scholarly journals Coefficient estimates for certain subclasses of spiral-like functions of complex order

2010 ◽  
Vol 23 (7) ◽  
pp. 763-768 ◽  
Author(s):  
H.M. Srivastava ◽  
Qing-Hua Xu ◽  
Guang-Ping Wu
Keyword(s):  
Coefficient Estimates ◽  
Complex Order

Coefficient estimates for a subclass of parabolic bi-starlike functions

2018 ◽  
Vol 29 (3-4) ◽  
pp. 331-338
Author(s):  
Serap Bulut
Keyword(s):  
Starlike Functions ◽  
Coefficient Estimates
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