On Analysis of Growth and Distortion Criteria for Certain Univalent Functions on the Unit Disk

Authors

  • Peter Ogol Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.
  • Titus Aminer Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.
  • Benard Okelo Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.

Keywords:

Growth, Distortion, Univalent function, Unit Disk

Abstract

Studies on growth and distortion conditions (GDC) for univalent functions (UF) in the unit disk (UD) have been conducted over decades with interesting findings obtained for various functions like the conformal mappings and slice regular functions with nice and very crucial in applications in various fields. However, complete analysis of these conditions has not been done. Recently, researchers gave an open question on the growth and distortion theorems asking whether the family of regular slice mappings is the largest subfamily of the unit ball of UF. In this paper, we analyze the GDC for UF in the UD. In particular, we consider the Koebe function (KF) and establish the its GDC by establishing its minimal and maximal extremal boundary points.

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Published

2025-07-08

Issue

Vol. 18 No. 3 (2025): Int. J. Open Problems Compt. Math., Vol. 18, No. 3, September 2025

Section

Articles