UNIVALENCE CRITERIA AND ANALOGUES OF THE JOHN CONSTANT

Title
UNIVALENCE CRITERIA AND ANALOGUES OF THE JOHN CONSTANT
Author(s)
김용찬Toshiyuki Sugawa[Toshiyuki Sugawa]
Issue Date
201312
Publisher
CAMBRIDGE UNIV PRESS
Citation
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, v.88, no.3, pp.423 - 434
Abstract
Let p(z) = zf'(z)/f(z) for a function f(z) analytic on the unit disc vertical bar z vertical bar< 1 in the complex plane and normalised by f(0) = 0, f'(0) = 1. We provide lower and upper bounds for the best constants delta(0) and delta(1) such that the conditions e(-delta 0/2) <vertical bar p(z) vertical bar<e(delta 0/2) and vertical bar p(w)/p(z)vertical bar< e(delta 1) for vertical bar z vertical bar, vertical bar w vertical bar< 1 respectively imply univalence of f on the unit disc.
URI
http://hdl.handle.net/YU.REPOSITORY/28010http://dx.doi.org/10.1017/S0004972712000962
ISSN
0004-9727
Appears in Collections:
사범대학 > 수학교육과 > Articles
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