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Fekete and Szegö inequality for a subclass of almost spirallike mappings of type β and order α on the bounded starlike circular domain in ℂn.
- Source :
- Complex Variables & Elliptic Equations; Jan2024, Vol. 69 Issue 1, p22-34, 13p
- Publication Year :
- 2024
-
Abstract
- Let $ \hat {\mathcal {S}}_{(\alpha,\beta)} $ S ^ (α , β) be the familiar class of almost spirallike functions of type β and order α in the unit disk (see Definition 1.1). In this paper, first, we prove that for a function $ f(z)=z+\sum _{n=2}^\infty a_nz^n $ f (z) = z + ∑ n = 2 ∞ a n z n in the class $ \hat {\mathcal {S}}_{(\alpha,\beta)} $ S ^ (α , β) , then $$\begin{align*} & |a_{3}-\lambda a_{2}^2|\\ & \quad \leq (1-\alpha)\cos{\beta}\max\{1,|1-4(1-\alpha)(1-\lambda)\cos{\beta}\,{\rm e}^{{\rm i}\beta}|\},\quad \lambda\in \mathbb{C}. \end{align*} $$ | a 3 − λ a 2 2 | ≤ (1 − α) cos β max { 1 , | 1 − 4 (1 − α) (1 − λ) cos β e i β | } , λ ∈ C. The above estimation is sharp. Second, we extend this result to the bounded starlike circular domain in $ \mathbb {C}^{n} $ C n and obtain the sharp estimates. The results presented here would provide extensions of those given by Xu et al. [The Fekete and Szegö problem on the bounded starlike circular domain in $ \mathbb {C}^n $ C n . Pure Appl Math Q. 2016;12:621–638] and Xiong [Sharp coefficients bounds for class of almost starlike mappings of order α in $ \mathbb {C}^n $ C n . J Math Inequalities. 2020;14:853–865]. Finally, a certain conjecture is also formulated. [ABSTRACT FROM AUTHOR]
- Subjects :
- LOGICAL prediction
MATHEMATICS
STAR-like functions
Subjects
Details
- Language :
- English
- ISSN :
- 17476933
- Volume :
- 69
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Complex Variables & Elliptic Equations
- Publication Type :
- Academic Journal
- Accession number :
- 174159872
- Full Text :
- https://doi.org/10.1080/17476933.2022.2107634