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}
}