scholarly journals Subclasses of analytic functions with respect to symmetric and conjugate points

2011 ◽  
Vol 42 (1) ◽  
pp. 87-94
Author(s):  
C. Selvaraj ◽  
N. Vasanthi
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Conjugate Points ◽  
Coefficient Estimates ◽  
Convex And Starlike Functions

In this paper, we introduce new subclasses of convex and starlike functions with respect to other points. The coefficient estimates for these classes are obtained.

scholarly journals Estimates for coefficients of certain analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3539-3552 ◽  
Author(s):  
V. Ravichandran ◽  
Shelly Verma
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Coefficient Problem ◽  
Inverse Coefficient Problem ◽  
Coefficient Bounds ◽  
Inverse Functions ◽  
Inverse Coefficient

For -1 ? B ? 1 and A > B, let S*[A,B] denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions f defined by the subordination z f'(z)/f(z)< (1+Az)/(1+Bz) (?z?<1). For -1 ? B ? 1 < A, we investigate the inverse coefficient problem for functions in the class S*[A,B] and its meromorphic counter part. Also, for -1 ? B ? 1 < A, the sharp bounds for first five coefficients for inverse functions of generalized Janowski convex functions are determined. A simple and precise proof for inverse coefficient estimations for generalized Janowski convex functions is provided for the case A = 2?-1(?>1) and B = 1. As an application, for F:= f-1, A = 2?-1 (?>1) and B = 1, the sharp coefficient bounds of F/F' are obtained when f is a generalized Janowski starlike or generalized Janowski convex function. Further, we provide the sharp coefficient estimates for inverse functions of normalized analytic functions f satisfying f'(z)< (1+z)/(1+Bz) (?z? < 1, -1 ? B < 1).

scholarly journals Multivalent Functions Related with an Integral Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Syed Ghoos Ali Shah ◽  
Saqib Hussain ◽  
Saima Noor ◽  
Maslina Darus ◽  
Ibrar Ahmad
Keyword(s):  
Integral Operator ◽  
Hadamard Product ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Rate Of Growth ◽  
Convex And Starlike Functions

In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature.

scholarly journals ON A CLASS OF MEROMORPHIC STARLIKE FUNCTIONS WITH NEGATIVE COEFFICIENTS

1996 ◽  
Vol 27 (1) ◽  
pp. 15-26
Author(s):  
K. K. DIXIT ◽  
S. K. PAL
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Integral Transforms ◽  
Coefficient Estimates ◽  
Linear Combinations ◽  
Meromorphic Starlike Functions ◽  
Class Of Functions

Let $T^*_M(A, B, z_0)$ denote the class of functions \[f(z)=\frac{a}{z}-\sum_{n=1}^\infty a_nz^n, a\ge 1, a_n\ge 0\] regular and univalent in unit disc $U'=\{z:0<|z|<1\}$, satisfying the condition \[-z\frac{f'(z)}{f(z)}=\frac{1+Aw(z)}{1+Bw(z)}, \quad \text{ for } z\in U' \text{ and } w\in E\] (where $E$ is the class of analytic functions $w$ with $w(0) = 0$ and $|w(z)| \le 1$), where $-1\le A < B \le 1$, $0\le B \le 1$ and $f(z_0) =1/z_0$ ($0<z_0<1$). In this paper sharp coefficient estimates, distortion properties and radius of meromorphic convexity for functions in $T^*_M(A, B, z_0)$ have been obtained. We also study integral transforms of functions in $T^*_M(A, B, z_0)$. In the last, it is proved that the class $T^*_M(A, B, z_0)$ is closed under convex linear combinations.          

scholarly journals Piggyback-Dualitäten

1985 ◽  
Vol 32 (1) ◽  
pp. 1-32 ◽  
Author(s):  
B.A. Davey ◽  
H. Werner
Keyword(s):  
Series Expansion ◽  
Analytic Functions ◽  
Laurent Series ◽  
Integral Operators ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Radius Of Convexity ◽  
Distortion Theorems ◽  
Convolution Properties

For the class of meromorphically starlike functions of prescribed order, the concept of type has been introduced. A characterization of meromorphically starlike functions of order α and type β has been obtained when the coefficients in its Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, radius of convexity estimates, integral operators, convolution properties et cetera for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.

scholarly journals New classes of $k$-uniformly convex and starlike functions

2004 ◽  
Vol 35 (3) ◽  
pp. 261-266 ◽  
Author(s):  
Essam Aqlan ◽  
Jay M. Jahangiri ◽  
S. R. Kulkarni
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Radius Of Starlikeness ◽  
Distortion Bounds ◽  
Convex And Starlike Functions

Certain classes of analytic functions are defined which will generalize new, as well as well-known, classes of k-uniformly convex and starlike functions. We provide necessary and sufficent coefficient conditions, distortion bounds, extreme points and radius of starlikeness for these classes.

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 New Subclasses of Analytic Functions with Respect to Symmetric and Conjugate Points

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Huo Tang ◽  
Guan-Tie Deng
Keyword(s):  
Analytic Functions ◽  
Conjugate Points ◽  
Quasiconvex Functions ◽  
Coefficient Estimates

We introduce new subclasses of close-to-convex and quasiconvex functions with respect to symmetric and conjugate points. The coefficient estimates for functions belonging to these classes are obtained.

scholarly journals Coefficient estimates for certain subclass of analytic functions defined by subordination

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3307-3318
Author(s):  
Nirupam Ghosh ◽  
A. Vasudevarao
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Open Problems ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions

In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with some open problems proposed by Q.H. Xu et al.([20], [21]). An application of Jack lemma for certain subclass of starlike functions has been discussed.

scholarly journals Some properties of starlike functions with respect to symmetric-conjugate points

1995 ◽  
Vol 18 (3) ◽  
pp. 469-474 ◽  
Author(s):  
Hassoon Al-Amiri ◽  
Dan coman ◽  
Petru T. Mocanu
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Conjugate Points ◽  
Sufficient Condition

LetAbe tile class of all analytic functions in the unit diskUsuch thatf(0)=f′(0)−1=0. A functionf∈Ais called starlike with respect to2nsymmetric-conjugate points ifRezf′(z)/fn(z)>0forz∈U, wherefn(z)=12n∑k=0n−1[ω−kf(ωkz)+ωkf(ωkz˜)¯],ω=exp(2πi/n]. This class is denoted bySn*, and was studied in [1]. A sufficient condition for starlikeness with respect to symmetric-conjugate points is obtained. In addition, images of some subclasses ofSn*under the integral operatorI:A→A,I(f)=FwhereF(z)=c+1(g(z))c∫0zf(t)(g(t))c−1g′(t)dt,   c>0andg∈Ais given are determined.

scholarly journals Coefficient estimates for new subclasses of analytic functions with respect to other points

2013 ◽  
Vol 44 (2) ◽  
pp. 141-148
Author(s):  
Huo Tang ◽  
Guan-tie Deng
Keyword(s):  
Analytic Functions ◽  
Conjugate Points ◽  
Coefficient Estimates

The main purpose of this paper is to derive coefficient estimates for new subclasses of analytic functions with respect to symmetric and conjugate points.

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