On differential subordinations related to convex functions
type: Item
instance of: scholarly article
title: On differential subordinations related to convex functions
zbMATH Open document ID: 0929.30019
author: Adam Lecko
author: Yong Chan Kim
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-10-25T00:00:00Z
review text: Let \(S^c\) denote the class of all convex functions \(h\) in the unit disc \(U=\{z:| z|<1\}\) and normalized \(f(0)=f'(0)-1=0\) and let \(S^c_0\) denote the subclass of \(S^c\) of such functions \(h\) that there exists a boundary point \(Q\) of \(h(U)\) lying in \((-\infty,0)\) and the line going through \(Q\) and parallel to the imaginary axis is a supporting line of \(h(U)\). In the paper the following result is proved: Theorem. Let \(\alpha\in[0,1]\), \(\beta\in[\alpha,1]\), \(h\in S^c_0\) and let \(p\) be analytic in \(U,p(0)=0\), \(p(z)\not\equiv 0\) such that a function \(P(z)=p(z)[1+{zp'(z)\over p(z)}]^\beta\) is well defined in \(U\), where the power has the principal value. If \(P(z)\prec({3\over 2})^\alpha h(z)\) then \(p(z)\prec h(z)\) where ``\(\prec\)'' denotes the subordination in the unit disc. Some other similar problems are also investigated.
reviewed by: Jan Stankiewicz
Mathematics Subject Classification ID: 30C80
Mathematics Subject Classification ID: 30C75
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1332879
zbMATH Keywords: differential subordination
zbMATH Keywords: convex function
Wikidata QID: Q59108710
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6381
OpenAlex ID: W2007129626
cites work: Q5581251
cites work: Convexity Preservation of Inverse Euler Operators and a Problem of S. Miller
cites work: Differential subordinations and geometric means
cites work: Differential subordinations and univalent functions
cites work: On some classes of first-order differential subordinations
cites work: Q4873946
cites work: Q4052427
DOI: 10.1006/JMAA.1999.6381
Recommended article: Q3812511
Recommended article: Q4300002
Recommended article: Q4336962
Recommended article: Differential subordinations and \(\alpha\)-convex functions
Recommended article: Q4950663
Recommended article: Q3679792
Recommended article: Convex functions, subdifferentiability and renormings
Recommended article: Q5289973
Recommended article: ON CERTAIN SUBCLASS OF CONVEX FUNCTIONS
Recommended article: Q3317321
description: scientific article; zbMATH DE number 1332879