English

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}
}
R2 v1 2026-06-21T23:35:44.911Z