Linear Combinations of Harmonic Univalent Mappings Convex In The Horizontal Direction

Demirçay M., Yaşar E.

1st International Conference on Engineering and Applied Natural Sciences, Konya, Turkey, 10 - 13 May 2022, pp.1595

  • Publication Type: Conference Paper / Summary Text
  • City: Konya
  • Country: Turkey
  • Page Numbers: pp.1595

Abstract

A domain is said to be convex in the horizontal direction (CHD) if every line parallel to the real

axis has either a connected or empty intersection with the domain. A harmonic and univalent function f in

the open unit disk E={z:|z|<1} is said to be a CHD mapping if f maps E onto a CHD domain. In this paper,

we consider two harmonic, univalent, and vertical strip mappings and we prove that the linear combination

of these two harmonic mappings is harmonic, univalent, and CHD if the linear combination is locally

univalent and sense-preserving.