Neighborhood of a Class of Analytic Functions with Negative Coefficients Defined by the Generalized Ruschewey Derivatives Involving a General Fractional Derivative Operator

Abstract

By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relations associated with the (n;δ)-neighborhoods of various subclasses of starlike and convex functions of complex order defined by the generalized Ruscheweyh derivative involving a general fractional derivative operator. Special cases of some of these inclusion relations are shown to yield known results.

Keywords. Analytic functions, Identity function, Starlike functions, Convex functions, Generalized Ruscheweyh derivative, Fractional drivative operator, Inclusion relations.

AMS Subject Classification [2000]. Primary 40H05 , Secondary 46A45