Linear operators associated with k-uniformly convex functions

Abstract

In terms of the Hadmard product (or convolution), define the operator by , where the function f is analytic in the unit disk. The classes of k-uniformly convex and k-starlike functions , denoted by , respectively, were introduced recently (cf.[3] and [5]). The object of the present paper is to find conditions on the papameters a,b,c, and k, for which the linear operator maps the classes of starlike and univalent functions onto .

Keywords:

• k-uniformly convex functions
• univalent functions
• k-starlike functions
• Hypergeometric functions
• Hadamard product (or convolution)
• integral operator
• Carlson-Shaffer operator
• Ruscheweyh derivative

MSC(1991):

• 30C45
• 33E05