Bulletin of the Belgian Mathematical Society - Simon Stevin

Starlikeness and convexity of polyharmonic mappings

J. Chen, A. Rasila, and X. Wang

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Abstract

In this paper, we first find an estimate for the range of polyharmonic mappings in the class $HC_{p}^{0}$. Then, we obtain two characterizations in terms of the convolution for polyharmonic mappings to be starlike of order $\alpha$, and convex of order $\beta$, respectively. Finally, we study the radii of starlikeness and convexity for polyharmonic mappings, under certain coefficient conditions.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 1 (2014), 67-82.

Dates
First available in Project Euclid: 11 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1394544295

Digital Object Identifier
doi:10.36045/bbms/1394544295

Mathematical Reviews number (MathSciNet)
MR3178531

Zentralblatt MATH identifier
1297.31008

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C20: Conformal mappings of special domains 30C65: Quasiconformal mappings in $R^n$ , other generalizations

Keywords
polyharmonic mapping starlike convex

Citation

Chen, J.; Rasila, A.; Wang, X. Starlikeness and convexity of polyharmonic mappings. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 1, 67--82. doi:10.36045/bbms/1394544295. https://projecteuclid.org/euclid.bbms/1394544295


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