dc.contributor.author |
Avkhadiev F. |
|
dc.contributor.author |
Wirths K. |
|
dc.date.accessioned |
2018-09-18T20:34:27Z |
|
dc.date.available |
2018-09-18T20:34:27Z |
|
dc.date.issued |
2010 |
|
dc.identifier.issn |
1995-0802 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/141281 |
|
dc.description.abstract |
Let f be holomorpic and univalent in the unit disc E and f(E) be convex. We consider the conformal radius R = R(D,z) = {pipe;} f′(ζ){pipe;}(1-ζ̄) of D = f(E) at the point z = f(ζ). In [3] and [4] the coefficient kf(r), r ∈ (0,1), of quasiconformality has been defined by the equation, In this paper the authors computed the quantity kf(r) for some convex functions. These examples led them to the conjecture that kf (r) ≤ r2 for any convex function holomorphic in E. The function f(ζ) = log((1 + ζ)/(1 -ζ)), which was among their examples, shows that this bound is sharp for any r∈ (0,1). In the present article, we will prove that the above conjecture is true and that the the above example is essentially the only one for which equality is attained. © 2010 Pleiades Publishing, Ltd. |
|
dc.relation.ispartofseries |
Lobachevskii Journal of Mathematics |
|
dc.subject |
Coefficient of quasiconformality |
|
dc.subject |
Conformal radius |
|
dc.subject |
Convex functions |
|
dc.title |
On the Coefficients of Quasiconformality for Convex Functions |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
4 |
|
dc.relation.ispartofseries-volume |
31 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
323 |
|
dc.source.id |
SCOPUS19950802-2010-31-4-SID78650045926 |
|