Abstract
The purpose of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some integral preserving properties are also considered.
Highlights
Let A denote the class of functions of the form fz z ak zk k2 which are analytic in the open unit disk U {z ∈ C : |z| < 1}
If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z if there exists an analytic function w in U with w 0 0 and |w z | < 1 for z ∈ U such that fzgwz
We denote by S∗, K, and C the subclasses of A consisting of all analytic functions which are, respectively, starlike, convex, and close-to-convex in U
Summary
The purpose of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions associated with a family of linear operators, which are defined by means of the Hadamard product or convolution.
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