Close-to-Convexity of Convolutions of Classes of Harmonic Functions

For j=1,2 and for positive integers m and n, we consider classes of harmonic functions fj=hj+gj¯, where g1(z)=znh1(z) and g2′(z)=znh2′(z) or g1′(z)=znh1′(z) and g2′(z)=zmh2′(z), and we prove that their convolution f1⁎f2=h1⁎h2+g1⁎g2¯ is locally one-to-one, sense-preserving, and close-to-convex harmon...

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Bibliographic Details
Published in:International journal of mathematics and mathematical sciences 2018, Vol.2018 (2018), p.1-4
Main Authors: Garg, Raj Kumar, M. Jahangiri, Jay
Format: Article
Language:English
Subjects:
Convexity
Convolution
Harmonic functions
Inequality
Integers
Theorems
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Summary:For j=1,2 and for positive integers m and n, we consider classes of harmonic functions fj=hj+gj¯, where g1(z)=znh1(z) and g2′(z)=znh2′(z) or g1′(z)=znh1′(z) and g2′(z)=zmh2′(z), and we prove that their convolution f1⁎f2=h1⁎h2+g1⁎g2¯ is locally one-to-one, sense-preserving, and close-to-convex harmonic in z
ISSN:0161-1712
1687-0425
DOI:10.1155/2018/3808513