Some Geometric Properties of a Hyperbolic Univalent Function

  • Sabah S. Al-Azawee Department of Mathematics, College of Sciences, Mustansiriyah University, Baghdad, Iraq
  • Shatha S. Alhily Department of Mathematics, College of Sciences, Mustansiriyah University, Baghdad, Iraq
Keywords: univalent function, convex function, convex region, hyperbolic metric space

Abstract

In this paper, we analyze several aspects of a hyperbolic univalent function related to convexity properties, by assuming  to be the univalent holomorphic function maps of the unit disk  onto the hyperbolic convex region  ( is an open connected subset of). This assumption leads to the coverage of some of the findings that are started by seeking a convex univalent function distortion property to provide an approximation of the inequality and confirm the form of the lower bound for . A further result was reached by combining the distortion and growth properties for increasing inequality  . From the last result, we wanted to demonstrate the effect of the unit disk image on the condition of convexity estimation by proving the two inequalities of

 , and   .

Published
2021-07-01
How to Cite
Al-Azawee, S. S., & Alhily , S. S. (2021). Some Geometric Properties of a Hyperbolic Univalent Function. Iraqi Journal of Science, 62(6), 2022-2028. https://doi.org/10.24996/ijs.2021.62.6.28
Section
Mathematics