Convolutions for special classes of harmonic univalent functions

Ruscheweyh and Sheil-Small proved the PólyarSchoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that close-to-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic...

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Bibliographic Details
Published in:Applied mathematics letters 2003-08, Vol.16 (6), p.905-909
Main Authors: Ahuja, O.P., Jahangiri, J.M., Silverman, H.
Format: Article
Language:English
Subjects:
Close-to-convex
Convex
Convolution
Exact sciences and technology
Functional analysis
Harmonic
Mathematical analysis
Mathematics
Sciences and techniques of general use
Starlike
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Summary:Ruscheweyh and Sheil-Small proved the PólyarSchoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that close-to-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form certain harmonic functions which preserve close-to-convexity under convolution. An auxiliary function enables us to obtain necessary and sufficient convolution conditions for convex and starlike harmonic functions, which lead to sufficient coefficient bounds for inclusion in these classes.
ISSN:0893-9659
1873-5452
DOI:10.1016/S0893-9659(03)90015-2