## Starlike of order Ξ± Convex of order Ξ± a b s t r a c t For analytic functions f (z) in the open unit disk U, there are many sufficient conditions for f (z) to be starlike and convex in U. In view of the paper by P.T. Mocanu [P.T. Mocanu, Some starlikeness conditions for analytic functions, Rev.
Some simple sufficient conditions for starlikeness and convexity
β Scribed by Nikola Tuneski
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 371 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
Let A be the class of analytic functions in the unit disc that are of the form
are studied, as sufficient conditions for starlikeness and convexity.
π SIMILAR VOLUMES
By making use of the Hadamard product (or convolution), the authors derive necessary and sufficient conditions for a suitably normalized meromorphically p-valent function to be in the familiar classes of meromorphic p-valently starlike and meromorphic p-valently convex functions in the punctured uni
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
The absence of atoms in Lyapunov's Convexity Theorem is a sufficient, but not a necessary condition for the convexity of the range of an n-dimensional vector memure. In this paper algebraic and topological convexity conditions generalizing Lyapunov's Theorem are developed which are sufficient and ne
## Abstract In this paper, we will give a sufficient condition for locally univalent holomorphic functions on the unit disc . in C to be strongly starlike. Also, we will give sufficient conditions for locally biholomorphic mappings on the unit ball __B__ in a complex Banach space __X__ to be starli