Sahoo, Pravati; Singh, Saumya Starlikeness conditions for an integral operator. (English) Zbl 1180.30026 JIPAM, J. Inequal. Pure Appl. Math. 10, No. 3, Paper No. 77, 6 p. (2009). Summary: For fixed \(n\in \mathbb N\), let \(\Sigma_n\) denote the class of functions of the following form\[ f(z)=\frac{1}{z}+\sum_{k=n}^\infty a_kz^k, \] which are analytic in the punctured open unit disk \(\Delta^*=\{z\in \mathbb C: 0<| z| <1\}\). In the present paper we define and study an operator in\[ F(z)=\left[\frac{c+1-\mu}{z^{c+1}}\int_0^z\left(\frac{f(t)}{t}\right)^\mu t^{c+\mu} dt\right]^{\frac{1}{\mu}},\qquad \text{for }f\in \Sigma_n\text{ and }c+1-\mu>0. \] MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30D30 Meromorphic functions of one complex variable (general theory) Keywords:meromorphic function; differential subordination; starlike function; convex function PDFBibTeX XMLCite \textit{P. Sahoo} and \textit{S. Singh}, JIPAM, J. Inequal. Pure Appl. Math. 10, No. 3, Paper No. 77, 6 p. (2009; Zbl 1180.30026) Full Text: EuDML EMIS