Certain Subclass of k-Uniformly p-Valent Starlike and Convex Functions Associated with Fractional Derivative Operators
Somia Muftah Amsheri *
Department of Mathematics, SCIM, University of Bradford, BD7 1DP, UK.
Valentina Zharkova
Department of Mathematics, SCIM, University of Bradford, BD7 1DP, UK.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we introduce a new subclass 
of k-uniformly p-valent starlike and convex functions in the open unit disk using a fractional differential operator. We obtain coefï¬cient estimates, distortion theorems, extermal properties, closure theorems, and inclusion properties. The radii for k-uniformly starlikeness, convexity and close-to-convexity for functions belonging to this class are also determined.
Keywords: p-valent function, starlike function, convex function, k-uniformly starlike function, k-uniformly convex function, fractional derivative operators