On polyharmonic univalent mappings

J. Chen, A. Rasila, X. Wang

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Abstract

In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by HSp(λ), and its subclass HS op(λ), where λ ∈ [0,1] is a constant. These classes are natural generalizations of a class of mappings studied by Goodman in the 1950s. We generalize the main results of Avci and Zlotkiewicz from the 1990s to the classes HSp(λ) and HSo p(λ), showing that the mappings in HSp(λ) are univalent and sense preserving. We also prove that the mappings in HS op(λ) are starlike with respect to the origin, and characterize the extremal points of the above classes.

Original languageEnglish
Pages (from-to)343-357
Number of pages15
JournalMathematical Reports
Volume15
Issue number4
StatePublished - 2013
Externally publishedYes

Keywords

  • Convexity
  • Extremal point
  • Polyharmonic mapping
  • Starlikeness

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