Back to Search
Start Over
Radius of concavity for certain class of functions
- Publication Year :
- 2024
-
Abstract
- Let $ \mathcal{S}(p) $ be the class of all meromorphic univalent functions defined in the unit disc $ \mathbb{D} $ of the complex plane with a simple pole at $ z=p $ and normalized by the conditions $ f(0)=0 $ and $ f^{\prime}(0)=1 $. In this paper, we find radius of concavity and compute the same for functions in $ \mathcal{S}(p) $ and for some other well-known classes of functions on unit disk. We explore general linear combinations $F(z):=\lambda_1f_1(z)+\cdots+\lambda_{2n} f_{2n}(z),\; \lambda_j\in\mathbb{C} $, $ n\in\mathbb{N} $, of functions belonging to the class $\mathcal{S}(p)$ and some other classes of functions of analytic univalent functions and investigate their radii of univalence, convexity and concavity.
- Subjects :
- Mathematics - Complex Variables
30C45, 30C55
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.00457
- Document Type :
- Working Paper