Owa, Shigeyoshi On new classes of analytic functions with negative coefficients. (English) Zbl 0582.30009 Int. J. Math. Math. Sci. 7, 719-730 (1984). The author considers the class \(K^*_ n\), \(n\in {\mathbb{N}}\cup \{0\}\), consisting of functions f(z) which satisfy in the unit disc \(| z| <1\), the conditions: \[ 1)\quad f(z)=z-\sum^{\infty}_{k=2}a_ kz^ k,\quad a_ k\geq 0,\quad and \]\[ 2)\quad Re\{D^{n+1} f(z)/D^ n f(z)\}>,\quad where\quad D^ n f(z)=f(z)*(z/(1-z)^{n+1}), \] (*) is the Hadamard product of power series. Coefficient inequalities, distortion and closure results are obtained. Reviewer: H.S.Al-Amiri Cited in 3 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:Ruscheweyh derivative; Hadamard product of power series; Coefficient inequalities; distortion PDFBibTeX XMLCite \textit{S. Owa}, Int. J. Math. Math. Sci. 7, 719--730 (1984; Zbl 0582.30009) Full Text: DOI EuDML