scholarly journals On sufficient conditions of meromorphic starlike functions

2014 ◽  
Vol 32 (2) ◽  
pp. 229
Author(s):  
Ali Muhammad
Keyword(s):  
Unit Disc ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Meromorphic Starlike Functions

In this paper, we investigate interesting properties and sufficient conditions for meromorphic starlike functions in the punctured unit disc.

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 On a class of analytic functions related to Robertson’s formula and subordination

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Growth Theorem

AbstractIn this paper, we define and study a class of analytic functions in the unit disc by modification of the well-known Robertson’s analytic formula for starlike functions with respect to a boundary point combined with subordination. An integral representation and growth theorem are proved. Early coefficients and the Fekete–Szegö functional are also estimated.

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

scholarly journals Convex and starlike criteria

1999 ◽  
Vol 22 (1) ◽  
pp. 75-79 ◽  
Author(s):  
Herb Silverman
Keyword(s):  
Sufficient Conditions ◽  
Starlike Functions ◽  
Positive Order ◽  
Convex And Starlike Functions

We investigate an expression involving the quotient of the analytic representations of convex and starlike functions. Sufficient conditions are found for functions to be starlike of a positive order and convex.

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 629 ◽  
Author(s):  
Muhammad Arif ◽  
Omar Barkub ◽  
Hari Srivastava ◽  
Saleem Abdullah ◽  
Sher Khan
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Partial Sums ◽  
Circular Region ◽  
Necessary And Sufficient ◽  
New Criterion ◽  
Symmetrical Points ◽  
Convexity Conditions

The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q-differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters.

scholarly journals Integral operators of certain univalent functions

1985 ◽  
Vol 8 (4) ◽  
pp. 653-662 ◽  
Author(s):  
O. P. Ahuja
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Univalent Functions ◽  
Integral Operators ◽  
Starlike Functions ◽  
The Family

A functionf, analytic in the unit discΔ, is said to be in the familyRn(α)ifRe{(znf(z))(n+1)/(zn−1f(z))(n)}>(n+α)/(n+1)for someα(0≤α<1)and for allzinΔ, wheren ϵ No,No={0,1,2,…}. The The classRn(α)contains the starlike functions of orderαforn≥0and the convex functions of orderαforn≥1. We study a class of integral operators defined onRn(α). Finally an argument theorem is proved.

scholarly journals Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Saibah Siregar ◽  
Maslina Darus
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Subordination Result ◽  
Jack’S Lemma ◽  
Jack's Lemma

For , , we consider the of normalized analytic convex functions defined in the open unit disc . In this paper, we investigate the class , that is, , with is Koebe type, that is, . The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class of -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

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