On a subclass of close-to-convex harmonic mappings

Yong Sun, Yue Ping Jiang, Antti Rasila*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

We introduce a new subclass M(α, β) of close-to-convex harmonic mappings in the unit disk, which originates from the work of P. Mocanu on univalent mappings. We also give coefficient estimates, and discuss the Fekete-Szegő problem, for this class of mappings. Furthermore, we consider growth, covering and area theorems of the class. In addition, we determine a disk |z| in which the partial sum sm,n(f)(z) is close-to-convex for each function of the class M(α, β). Finally, for certain values of the parameters α and β , we solve the radii problems related to starlikeness and convexity of functions of this class.

Original languageEnglish
Pages (from-to)1627-1643
Number of pages17
JournalCOMPLEX VARIABLES AND ELLIPTIC EQUATIONS
Volume61
Issue number12
DOIs
Publication statusPublished - 1 Dec 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • area theorem
  • close-to-convex function
  • coefficient estimate
  • convex function
  • covering theorem
  • Fekete–Szegő problem
  • growth theorem
  • Harmonic mapping
  • partial sum
  • starlike function

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