Some Geometric Properties of a Hyperbolic Univalent Function

Authors

  • 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

DOI:

https://doi.org/10.24996/ijs.2021.62.6.28

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   .

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Published

2021-07-01

Issue

Section

Mathematics

How to Cite

Some Geometric Properties of a Hyperbolic Univalent Function. (2021). Iraqi Journal of Science, 62(6), 2022-2028. https://doi.org/10.24996/ijs.2021.62.6.28

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