New extensions for a theorem by Mocanu
Complex Variables
2013-03-05 v1
Abstract
For analytic functions f(z) in the open unit disk U with f(0)=f'(0)-1=f"(0)=0, P. T. Mocanu (Mathematica (Cluj), 42(2000)) has considered some sufficient arguments of f'(z)+zf"(z) for |\arg(zf'(z)/f(z))|<\pi\mu/2. The object of the present paper is to discuss those probrems for f(z) with f"(0)=f"'(0)=...=f^{(n)}(0)=0 and f^{(n+1)}(0) \ne 0.
Keywords
Cite
@article{arxiv.1303.0513,
title = {New extensions for a theorem by Mocanu},
author = {Hitoshi Shiraishi and Shigeyoshi Owa},
journal= {arXiv preprint arXiv:1303.0513},
year = {2013}
}