Convex combinations of harmonic shears of slit mappings

Document Type : Research Paper


1 School of Mathematics and Statistics‎, ‎Anyang Normal University‎, ‎Anyang 455002‎, ‎Henan‎, ‎P‎.‎R‎. ‎China.

2 School of Mathematics and Computing Science‎, ‎Hunan First Normal University‎, ‎Changsha 410205‎, ‎Hunan‎, ‎P‎.‎R‎. ‎China.

3 Department of Mathematics and Systems Analysis‎, ‎Aalto University‎, ‎P‎.‎O‎. ‎Box 11100‎, ‎FI-00076 Aalto‎, ‎Finland.

4 School of Science‎, ‎Hunan Institute of Engineering‎, ‎Xiangtan 411104‎, ‎Hunan‎, ‎P‎.‎R‎. ‎China.


‎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.


Main Subjects

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