English

Properties of certain analytic functions associated with two boundary points

Complex Variables 2013-03-05 v1

Abstract

For analytic functions f(z) in the closed unit disk \bar{U}, two boundary points z_1 and z_2 such that \alpha = (f'(z_1)+f'(z_2))/2 in f'(U) are considered. The object of the present paper is to discuss some interesting conditions for f(z) to be |f'(z)-1|<\rho|1-\alpha| in U with some examples.

Keywords

Cite

@article{arxiv.1303.0506,
  title  = {Properties of certain analytic functions associated with two boundary points},
  author = {Hitoshi Shiraishi and Shigeyoshi Owa},
  journal= {arXiv preprint arXiv:1303.0506},
  year   = {2013}
}
R2 v1 2026-06-21T23:35:44.192Z