Starlikeness and convexity of polyharmonic mappings
Jiaolong Chen, Antti Rasila, Xiantao Wang
TL;DR
This paper investigates the geometric properties of polyharmonic mappings, providing estimates for their ranges, characterizations for starlikeness and convexity, and radii under coefficient conditions.
Contribution
It introduces new estimates, characterizations, and radius results for polyharmonic mappings related to starlikeness and convexity.
Findings
Range estimates for polyharmonic mappings in HC_p^0
Convolution characterizations for starlike and convex polyharmonic mappings
Radius results for starlikeness and convexity under coefficient conditions
Abstract
In this paper, we first find an estimate for the range of polyharmonic mappings in the class . Then, we obtain two characterizations in terms of the convolution for polyharmonic mappings to be starlike of order , and convex of order , respectively. Finally, we study the radii of starlikeness and convexity for polyharmonic mappings, under certain coefficient conditions.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Crystal Structures and Properties