Growth, Distortion, Pre-Schwarzian and Schwarzian norm estimates for Generalized Robertson class
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918240620380160 |
|---|---|
| author | Ahamed, Molla Basir Hossain, Rajesh |
| author_facet | Ahamed, Molla Basir Hossain, Rajesh |
| contents | This paper investigates the geometric properties of functions within the generalized Robertson class which consists of alpha-starlike functions of order beta. The study's significance lies in providing a deeper understanding of the univalence and geometric behavior of these functions, which are fundamental in complex analysis and geometric function theory. The primary objective is to derive sharp bounds for the norms of the Schwarzian and pre-Schwarzian derivatives for functions in this class. These bounds are expressed in terms of the initial coefficient of the function, specifically focusing on the important case where this initial coefficient is zero. Additionally, the paper establishes sharp distortion and growth theorems for the functions belonging to this generalized class. Finally, the research addresses the radius problem for this function class by determining the sharp radius of concavity and the sharp radius of convexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08993 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Growth, Distortion, Pre-Schwarzian and Schwarzian norm estimates for Generalized Robertson class Ahamed, Molla Basir Hossain, Rajesh Complex Variables 30C45, 30C55 This paper investigates the geometric properties of functions within the generalized Robertson class which consists of alpha-starlike functions of order beta. The study's significance lies in providing a deeper understanding of the univalence and geometric behavior of these functions, which are fundamental in complex analysis and geometric function theory. The primary objective is to derive sharp bounds for the norms of the Schwarzian and pre-Schwarzian derivatives for functions in this class. These bounds are expressed in terms of the initial coefficient of the function, specifically focusing on the important case where this initial coefficient is zero. Additionally, the paper establishes sharp distortion and growth theorems for the functions belonging to this generalized class. Finally, the research addresses the radius problem for this function class by determining the sharp radius of concavity and the sharp radius of convexity. |
| title | Growth, Distortion, Pre-Schwarzian and Schwarzian norm estimates for Generalized Robertson class |
| topic | Complex Variables 30C45, 30C55 |
| url | https://arxiv.org/abs/2512.08993 |