Copyright © 2012 Rosihan M. Ali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Sufficient conditions on a sequence of nonnegative numbers are obtained that ensures is starlike of nonnegative order in the unit disk. A result of Vietoris on trigonometric sums is extended in this pursuit. Conditions for close to convexity and convexity in the direction of the imaginary axis are also established. These results are applied to investigate the starlikeness of functions involving the Gaussian hypergeometric functions.