Close-to-convexity and starlikeness of analytic functions

Lee See Keong; V. Ravichandran; Shamani Supramaniam

Close-to-convexity and starlikeness of analytic functions

Complex Variables 2012-07-30 v1

Authors: Lee See Keong , V. Ravichandran , Shamani Supramaniam

Abstract

For functions $f(z)=z^p+a_{n+1}z^{p+1}+...$ defined on the open unit disk, the condition $\Re (f'(z)/z^{p-1})>0$ is sufficient for close-to-convexity of $f$ . By making use of this result, several sufficient conditions for close-to-convexity are investigated and relevant connections with previously known results are indicated.

Keywords

analytic functions close-to-convexity starlikeness unit disk sufficient conditions geometric function theory

Cite

@article{arxiv.1207.6495,
  title  = {Close-to-convexity and starlikeness of analytic functions},
  author = {Lee See Keong and V. Ravichandran and Shamani Supramaniam},
  journal= {arXiv preprint arXiv:1207.6495},
  year   = {2012}
}

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