Srivastava, H. M.; Mishra, A. K.; Das, M. K. A unified operator in fractional calculus and its applications to a nested class of analytic functions with negative coefficients. (English) Zbl 1019.30012 Complex Variables, Theory Appl. 40, No. 2, 119-132 (1999). Summary: By making use of a fractional differintegral operator \(\Omega^\lambda_z (-\infty <\lambda<1)\), which unifies the concepts of fractional derivative and fractional integral, we introduce and study a nested class \({\mathcal T}_\lambda (\alpha)\) \((0\leq \alpha<1)\) of analytic functions with negative coefficients. Various growth and distortion theorems, and some general results pertaining to the Strohäcker-Marx problem, are obtained for the class \({\mathcal T}_\lambda (\alpha)\). MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 26A33 Fractional derivatives and integrals Keywords:fractional derivative; fractional integral; starlike functions of order \(\alpha\); convex functions of order \(\alpha\); growth and distortion theorems; order of starlikeness PDFBibTeX XMLCite \textit{H. M. Srivastava} et al., Complex Variables, Theory Appl. 40, No. 2, 119--132 (1999; Zbl 1019.30012) Full Text: DOI