Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables

doi:10.1007/s11464-015-0496-5

Front. Math. China

2015, Vol. 10

Issue (6) : 1461-1472 https://doi.org/10.1007/s11464-015-0496-5

RESEARCH ARTICLE

Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables

Qinghua XU^1,^*(

),Ting YANG¹,Taishun LIU²,Huiming XU³

1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China
2. Department of Mathematics, Huzhou University, Huzhou 313000, China
3. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China

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Abstract

Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that max?f∈K|a3−λa22|≤max?{1/3,|λ−1|},λ∈?, and the estimate is sharp for each λ. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in ?n. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

Keywords Fekete-Szegö problem quasi-convex mappings of type A quasiconvex mappings of type B quasi-convex mappings of type C

Corresponding Author(s): Qinghua XU

Issue Date: 12 October 2015

Cite this article:

Qinghua XU,Ting YANG,Taishun LIU, et al. Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables[J]. Front. Math. China, 2015, 10(6): 1461-1472.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0496-5
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I6/1461

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