Campbell's conjecture on a majorization-subordination result for convex functions
type: Item
instance of: scholarly article
title: Campbell's conjecture on a majorization-subordination result for convex functions
zbMATH Open document ID: 0548.30007
DOI: 10.1216/RMJ-1984-14-2-331
author: Charles N. Kellogg
author: Roger W. Barnard
published in: Rocky Mountain Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: \textit{D. M. Campbell} [Trans. Am. Math. Soc. 198, 297-306 (1974; Zbl 0293.30015)] has shown that any f which is analytic in the unit disc, satisfies \(f'(0)\geq 0\) and is subordinate to an F belonging to the class of normalized analytic locally univalent functions of order \(\alpha\), \(1.65\leq\alpha,\) also satisfies \(| f'(z)|\leq | F'(z)|\) in \(| z| <\alpha +1+(\alpha^ 2+2\alpha)^{{1\over2}}.\) He conjectured that the theorem is true for \(1\leq\alpha <1.65,\) too. The authors confirm this for \(\alpha =1\), i.e. for the case of a convex F. Their method seems not to be applicable in the case \(1<\alpha <1.65.\)
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 3873649
zbMATH Keywords: convex functions
zbMATH Keywords: subordinate
MaRDI profile type: Publication
Wikidata QID: Q123200680
full work available at URL: rmj-1984-14-2-331
OpenAlex ID: W2068839981
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description: scientific article; zbMATH DE number 3873649