Linear Combination of Harmonic Strip Mappings

Yaşar E.

1st International Conference on Engineering and Applied Natural Sciences, Konya, Turkey, 10 - 13 May 2022, pp.1597

  • Publication Type: Conference Paper / Summary Text
  • City: Konya
  • Country: Turkey
  • Page Numbers: pp.1597


A harmonic and univalent function 𝑓=ℎ+𝑔̅ where h and g are analytic functions in the open unit disk E={z:|z|<1} is said to be a mapping convex in the horizontal domain (CHD) if f maps E onto a domain which has either a connected or empty intersection with the every line parallel to the real axis. The main object of this work is to investigate under which conditions linear combinations of harmonic and univalent vertical strip mappings can be harmonic, univalent and CHD mapping. A result is obtained due to this problem and an example is provided to illustrate the result.