Notes on the starlikeness of an integral transform

Authors

  • Jian-Lin Li

DOI:

https://doi.org/10.5556/j.tkjm.32.2001.358

Abstract

Let $ A $ denote the class of normalized analytic functions in the unit disk $ D $. For $ f(z) \in A $ and $ \alpha > 0 $, let $ F_{\alpha} (z) = \int_0^z (f(t)/t)^{\alpha} dt $ in $ D $. In this note, the author obtains the best constant $ \beta (\alpha) $ for each $ \alpha \in (0,3] $ such that Re$ \{ f'(z) (f(z)/z)^{\alpha -1} \} > \beta (\alpha) $ implies the starlikeness of $ F_{\alpha} (z) $.

Author Biography

Jian-Lin Li

Research Center for Science, Xi’an Jiaotong University, Xi’an, Shaan Xi 710049, P. R. China. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaan Xi 710072, P. R. China (Permanent address).

Published

2001-06-30

How to Cite

Li, J.-L. (2001). Notes on the starlikeness of an integral transform. Tamkang Journal of Mathematics, 32(2), 151-154. https://doi.org/10.5556/j.tkjm.32.2001.358

Issue

Section

Papers