Coefficient conditions for starlikeness of nonnegative order
Summary: Sufficient conditions on a sequence \(\{a_k\}\) of nonnegative numbers are obtained which ensure that \(f(z) = \sum^\infty_{k=1} a_k z^k\) 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 Gaussian hypergeometric functions.
scientific article; zbMATH DE number 6134092
scientific article