# On the Fekete and Szegö Inequality for a Subclass of Strongly Starlike Mappings of Order $${\varvec{\alpha }}$$ α

On the Fekete and Szegö Inequality for a Subclass of Strongly Starlike Mappings of Order... Let $$\mathcal {S}_\alpha ^*$$ S α ∗ be the familiar class of strongly starlike functions of order $$\alpha$$ α in the unit disk. In this paper, first, we prove the following result \begin{aligned} \max \limits _{f\in \mathcal {S}_\alpha ^*}|a_3-\lambda a_2^2|\le \alpha \max \{1,\ \alpha |3-4\lambda |\}, \ \lambda \in \mathbb {C}. \end{aligned} max f ∈ S α ∗ | a 3 - λ a 2 2 | ≤ α max { 1 , α | 3 - 4 λ | } , λ ∈ C . The above estimate is sharp for each $$\lambda$$ λ . Second, we generalize this result to several complex variables. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

# On the Fekete and Szegö Inequality for a Subclass of Strongly Starlike Mappings of Order $${\varvec{\alpha }}$$ α

, Volume 72 (2) – Feb 16, 2017
15 pages

/lp/springer_journal/on-the-fekete-and-szeg-inequality-for-a-subclass-of-strongly-starlike-SQwhtmRL9G
Publisher
Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-017-0650-3
Publisher site
See Article on Publisher Site

### Abstract

Let $$\mathcal {S}_\alpha ^*$$ S α ∗ be the familiar class of strongly starlike functions of order $$\alpha$$ α in the unit disk. In this paper, first, we prove the following result \begin{aligned} \max \limits _{f\in \mathcal {S}_\alpha ^*}|a_3-\lambda a_2^2|\le \alpha \max \{1,\ \alpha |3-4\lambda |\}, \ \lambda \in \mathbb {C}. \end{aligned} max f ∈ S α ∗ | a 3 - λ a 2 2 | ≤ α max { 1 , α | 3 - 4 λ | } , λ ∈ C . The above estimate is sharp for each $$\lambda$$ λ . Second, we generalize this result to several complex variables.

### Journal

Results in MathematicsSpringer Journals

Published: Feb 16, 2017

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