scholarly journals On a New Criterion for Meromorphic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Lei Shi ◽  
Zhi-Gang Wang
Keyword(s):  
Starlike Functions ◽  
New Criterion ◽  
Meromorphic Starlike Functions

The main purpose of this paper is to derive a new criterion for meromorphic starlike functions of orderα.

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 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 On meromorphic starlike functions

1963 ◽  
Vol 13 (1) ◽  
pp. 221-235 ◽  
Author(s):  
Christian Pommerenke
Keyword(s):  
Starlike Functions ◽  
Meromorphic Starlike Functions

scholarly journals Meromorphic starlike functions

1981 ◽  
Vol 11 (3) ◽  
pp. 441-458 ◽  
Author(s):  
Paul J. Eenigenburg ◽  
Albert E Livingston
Keyword(s):  
Starlike Functions ◽  
Meromorphic Starlike Functions

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 A new criterion for starlike functions

1996 ◽  
Vol 19 (3) ◽  
pp. 613-614 ◽  
Author(s):  
Ling Yi ◽  
Shusen Ding
Keyword(s):  
Starlike Functions ◽  
New Criterion

In this paper we shall get a new criterion for starlikeness, and the hypothesis of this criterion is much weaker than those in [1] and [2].

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