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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 |