Convex combinations of harmonic shears of slit mappings

Authors

  • A. Rasila Department of Mathematics and Systems Analysis‎, ‎Aalto University‎, ‎P‎.‎O‎. ‎Box 11100‎, ‎FI-00076 Aalto‎, ‎Finland.
  • L. Shi School of Mathematics and Statistics‎, ‎Anyang Normal University‎, ‎Anyang 455002‎, ‎Henan‎, ‎P‎.‎R‎. ‎China.
  • Y. Sun School of Science‎, ‎Hunan Institute of Engineering‎, ‎Xiangtan 411104‎, ‎Hunan‎, ‎P‎.‎R‎. ‎China.
  • Z.-G. Wang School of Mathematics and Computing Science‎, ‎Hunan First Normal University‎, ‎Changsha 410205‎, ‎Hunan‎, ‎P‎.‎R‎. ‎China.
Abstract:

‎In this paper‎, ‎we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings‎. ‎Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived‎. ‎Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate potential applications of the main results.

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Journal title

volume 43  issue 5

pages  1495- 1510

publication date 2017-10-31

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