We denote by A, the class of all analytic functions f in the unit disc β = {z β C : |z| < 1} with the normalization f (0) = f β² (0) -1 = 0. For a positive number Ξ» > 0, we denote by β A, such that a 3 -a 2 2 = 0, and satisfying the condition In this paper, we find conditions on Ξ», Ξ± and Ξ³ such tha
Janowski starlikeness for a class of analytic functions
β Scribed by Rosihan M. Ali; R. Chandrashekar; V. Ravichandran
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 216 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
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β¦ Synopsis
A normalized analytic function f defined on the open unit disk is a Janowski starlike
, where A and B are complex numbers satisfying the conditions |B| β€ 1 and A ΜΈ = B. In this paper, a new class of analytic functions defined by means of subordination is introduced. Sufficient conditions are obtained for functions in this class to be Janowski starlike. The results obtained extend earlier known works.
π SIMILAR VOLUMES
Let z be an analytic function with positive real part on β¬ s z; z -1 with Ε½ . Ε½ . 0 s 1, Π 0 ) 0 which maps the unit disk β¬ onto a region starlike with respect Ε½ . to 1 and symmetric with respect to the real axis. Let ST denote the class of Ε½ . Ε½ . Ε½ . Ε½ . Ε½ . Ε½ . analytic functions f z with f 0 s
A new criterion for starlikeness in the unit disc and an application to a certain class of rational functions are given.