Aouf, M. K. On a certain class of meromorphic univalent functions with positive coefficients. (English) Zbl 0745.30011 Rend. Mat. Appl., VII. Ser. 11, No. 2, 209-219 (1991). Let \(\Sigma_ p(\alpha,\beta,A,B,\gamma)\) (\(0\leq\alpha<1\), \(0<\beta\leq1\), \(-1\leq A<B\leq1\), \(0<B\leq1\), \({A\over A- B}\leq\gamma\leq 1\)) denote the class of meromorphic univalent functions \[ f(z)={1\over z}+\sum_{n=1}^ \infty a_ n z^ n \qquad (a_ n\geq0), \] in \(U^*=\{z:\;0<| z|<1\}\) and satisfying the condition \[ \left|{z^ 2f'(z)+1} \over {[(B-A)\gamma+A]z^ 2f'(z)+[(B-A)\gamma\alpha+A]} \right|<\beta. \] In this paper the author determines the coefficient estimates, distortion theorems, radii of starlikeness and convexity for the class \(\Sigma_ p(\alpha,\beta,A,B,\gamma)\). It is further shown that this class is closed under convex linear combinations and convolutions. Reviewer: R.M.Goel (Patiala) Cited in 15 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30C50 Coefficient problems for univalent and multivalent functions of one complex variable Keywords:distortion theorems; starlikeness; convexity PDFBibTeX XMLCite \textit{M. K. Aouf}, Rend. Mat. Appl., VII. Ser. 11, No. 2, 209--219 (1991; Zbl 0745.30011)