On the Fekete and Szegö problem for starlike mappings of order [alpha]

Let S [Stack ^sub [alpha] ^ ^sup *^ ] be the familiar class of normalized starlike functions of order [alpha] in the unit disk. In this paper, we establish the Fekete and Szegö inequality for the class S [Stack ^sub [alpha] ^ ^sup *^ ], and then we generalize this result to the unit ball in a comple...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 33; no. 4; p. 554
Main Authors Xu, Qing Hua, Fang, Fang, Liu, Tai Shun
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.04.2017
Subjects
Banach spaces
Estimates
Inequality
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Summary:Let S [Stack ^sub [alpha] ^ ^sup *^ ] be the familiar class of normalized starlike functions of order [alpha] in the unit disk. In this paper, we establish the Fekete and Szegö inequality for the class S [Stack ^sub [alpha] ^ ^sup *^ ], and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in C^sup n ^.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-5762-2