Some Transformation Properties with Omitted Value

Fatima AH. Mazloum; Shatha S. Alhily

doi:10.24996/ijs.2023.64.7.30

Authors

Fatima AH. Mazloum Department of Mathematics, College of Sciences, Mustansiriyah University, Baghdad, Iraq
Shatha S. Alhily Department of Mathematics, College of Sciences, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0002-8209-8421

DOI:

https://doi.org/10.24996/ijs.2023.64.7.30

Keywords:

Omitted- value transformation,, Univalent function, Convex univalent function, Starlike univalent function, Rotation property

Abstract

The purpose of this paper is to show that for a holomorphic and univalent function in class S, an omitted –value transformation yields a class of starlike functions as a rotation transformation of the Koebe function, allowing both the image and rotation of the function

to be connected. Furthermore, these functions have several properties that are not far from a convexity properties. We also show that Pre- Schwarzian derivative is not invariant since the convexity property of the function is so weak.