Some subclasses of analytic functions associated with fractional calculus operators

This paper begins by studying several properties and characteristics of cer tain subclasses of analytic functions with positive coefficients. The resul ts investigated here include various coefficient inequalities, distortion p roperties, and the radii of close-to-convexity. Inclusion theorems involvin g the Hardy space of analytic functions and the class of functions whose de rivative has a positive real part are also investigated. Relationships betw een certain subclasses of analytic functions (involving fractional derivati ve operators) with negative coefficients and a certain generalized fraction al integral operator are then studied. Various known or new special cases o f our results are also pointed out. (C) 1999 Elsevier Science Ltd. All righ ts reserved.