dc.contributor.author |
Avkhadiev F. |
|
dc.contributor.author |
Wirths K. |
|
dc.date.accessioned |
2018-09-18T20:22:05Z |
|
dc.date.available |
2018-09-18T20:22:05Z |
|
dc.date.issued |
2007 |
|
dc.identifier.issn |
1370-1444 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/139143 |
|
dc.description.abstract |
Let Ω and ∏ be two simply connected domains in the complex plane ℂ which are not equal to the whole plane ℂ. We are concerned with the set A(Ω, ∏) of functions f : Ω → ∏ holomorphic on Ω and we prove estimates for |f(n)(z)|, f ∈ A (ω, ∏), z ∈ Ω, of the following type. Let λ Ω(z) and λ∏(w) denote the density of the Poincaré metric of Ω at z and of ∏ at w, respectively. Then for any pair (Ω, ∏) where Ω is convex, f ∈ A(Ω, ∏), z ∈ Ω, and n > 2 the inequality |f(n)(z)|/n! ≤ (n+1)2n-2 (λΩ(z))n/ λ∏(f(z)) is valid. For functions f ∈ A(Ω, ∏), which are injective on Ω, the validity of above inequality was conjectured by Chua in 1996. |
|
dc.relation.ispartofseries |
Bulletin of the Belgian Mathematical Society - Simon Stevin |
|
dc.subject |
Convex domain |
|
dc.subject |
Poincaré metric |
|
dc.subject |
Simply connected domain |
|
dc.subject |
Taylor coefficients |
|
dc.title |
Punishing factors and Chua's conjecture |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
2 |
|
dc.relation.ispartofseries-volume |
14 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
333 |
|
dc.source.id |
SCOPUS13701444-2007-14-2-SID34547829727 |
|