Uralegaddi, B. A.; Sarangi, S. M. Some classes of univalent functions with negative coefficients. (English) Zbl 0671.30013 An. Științ. Univ. Al. I. Cuza Iași, N. Ser., Secț. Ia 34, No. 1, 7-11 (1988). Let A denote the class of functions f of the form \(f(z)=z+\sum^{\infty}_{k=2}a_ kz^ k\) analytic in the unit disk \(\{z=z:\) \(| z| <1\}.\) Let \(D^ nf(z)=z/(1-z)^{n+1}*f(z)\) (* denotes the Hadamard product), \(n=0,1,2,... \). Denote by \(K_ n\) the set of all functions \(f\in A\) satisfying \(Re(D^{n+1}f(z)/D^ nf(z))>1/2\), \(z\in E\). The class \(K_ n\) was introduced and studied by Ruscheweyh. Let T denote the subclass of A consisting of functions f of the form \(f(z)=z-\sum^{\infty}_{2}a_ kz^ k\) \((a_ k\geq 0)\) which are univalent in E and \(Q_ n[\alpha]\), \(0\leq \alpha <1\) denote the subclass of T whose members satisfy \(Re(D^ nf(z))'>\alpha\) for \(z\in E\). In this paper some properties of \(Q_ n[\alpha]\) are studied. Reviewer: K.S.Padmanabhan Cited in 1 ReviewCited in 3 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:functions with negative coefficients; Hadamard product PDFBibTeX XMLCite \textit{B. A. Uralegaddi} and \textit{S. M. Sarangi}, An. Științ. Univ. Al. I. Cuza Iași, N. Ser., Secț. Ia 34, No. 1, 7--11 (1988; Zbl 0671.30013)