Owa, Shigeyoshi; Fukui, Seiichi; Sakaguchi, Koichi; Ogawa, Shotaro An application of the Ruscheweyh derivatives. (English) Zbl 0613.30013 Int. J. Math. Math. Sci. 9, 721-730 (1986). Let \(D^{\alpha}f(z)\) be the Ruscheweyh derivative defined by using the Hadamard product of f(z) and \(z/(1-z)^{1+\alpha}\). Certain new classes \(S^*_{\alpha}\) and \(K_{\alpha}\) are introduced by virtue of the Ruscheweyh derivative. The object of the present paper is to establish several interesting properties of \(S^*_{\alpha}\) and \(K_{\alpha}\) (see the review below). Further, some results for integral operator \(J_ c(f)\) of f(z) are shown. Cited in 2 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:starlike function; convex function; Ruscheweyh derivative; Hadamard product; integral operator Citations:Zbl 0613.30014 PDFBibTeX XMLCite \textit{S. Owa} et al., Int. J. Math. Math. Sci. 9, 721--730 (1986; Zbl 0613.30013) Full Text: DOI EuDML