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doi:10.1016/j.aml.2005.06.005 
Copyright © 2005 Elsevier Ltd All rights reserved.
Convolution and subordination in the convex hull of convex mappings
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Janusz Sokół
Received 7 January 2005;
accepted 6 June 2005.
Available online 2 September 2005.
Abstract
In this work we give an extension of the Ruscheweyh and Stankiewicz theorem [S. Ruscheweyh, J. Stankiewicz, Subordination under convex univalent functions, Bull. Polish Acad. Sci. Math. 33 (1985) 499–502] on the subordination under convex functions in the unit disc Δ={z:|z|<1}. We prove that if and
, then f
g
FG where denotes the subordination, denotes the Hadamard product and is the closed convex hull of the class of convex functions.
Keywords: Convex function; Convex hull; Starlike function; Subordination; Convolution (Hadamard product)
MSC: primary; 30C45; secondary; 30C55
