Abstract
Making use of a linear operator Iλp(a,c), which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion properties of these subclasses. Some radius problems are also discussed.
Highlights
Introduction and DefinitionsLet p denote the class of functions f z of the form f z = z p ap k z p k ( p : {1, 2,3, }), (1)k =1 which are analytic in the open unit disk= z : z and z < 1 .We define the Hadamard product of two analytic functions f z = ak zk and g z = bk zk, k =0 k =0 as f g z : akbk zk z . k =0For a, c 0 ( 0 :, 2, 1, 0 ) H
K =1 which are analytic in the open unit disk
A, c; z is the function defined in terms of the Hadamard product by the following condition a, c; z a, c; z
Summary
We define the Hadamard product (or convolution) of two analytic functions In [3], Cho et al introduced the following family of linear operators A, c; z is the function defined in terms of the Hadamard product (or convolution) by the following condition a, c; z a, c; z Let k be the class of functions h z analytic in the unit disk satisfying the properties h 0 = 1 and
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