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Support points for families of univalent mappings on bounded symmetric domains
- Source :
- Science China Mathematics. 63:2379-2398
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper we study some extremal problems for the family $S_g^0(\mathbb{B}_X)$ of normalized univalent mappings with $g$-parametric representation on the unit ball $\mathbb{B}_X$ of an $n$-dimensional JB$^*$-triple $X$ with $r\geq 2$, where $r$ is the rank of $X$ and $g$ is a convex (univalent) function on the unit disc $\mathbb{U}$, which satisfies some natural assumptions. We obtain sharp coefficient bounds for the family $S_g^0(\mathbb{B}_X)$, and examples of bounded support points for various subsets of $S_g^0(\mathbb{B}_X)$. Our results are generalizations to bounded symmetric domains of known recent results related to support points for families of univalent mappings on the Euclidean unit ball $\mathbb{B}^n$ and the unit polydisc $\mathbb{U}^n$ in $\mathbb{C}^n$. Certain questions will be also mentioned. Finally, we point out sharp coefficient bounds and bounded support points for the family $S_g^0(\mathbb{B}^n)$ and for special compact subsets of $S_g^0(\mathbb{B}^n)$, in the case $n\geq 2$.<br />SCIENCE CHINA Mathematics
- Subjects :
- Unit sphere
Mathematics - Complex Variables
General Mathematics
010102 general mathematics
Regular polygon
Function (mathematics)
Rank (differential topology)
Polydisc
01 natural sciences
010101 applied mathematics
Combinatorics
Bounded function
Euclidean geometry
FOS: Mathematics
Complex Variables (math.CV)
0101 mathematics
Unit (ring theory)
Mathematics
Subjects
Details
- ISSN :
- 18691862 and 16747283
- Volume :
- 63
- Database :
- OpenAIRE
- Journal :
- Science China Mathematics
- Accession number :
- edsair.doi.dedup.....744e2bf317e786ebdce127eae64109b3