A Subclass of Uniformly Convex Functions and a Corresponding Subclass of Starlike Functions with Fixed Second Coefficient Defined by Carlson and Shaffer …

International Mathematical Forum 01/2010; 5(37):1839-1848.

ABSTRACT The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and correspond-ing subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f (z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f (z) in UCT (α, β) by fixing second coefficient.

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