Abstract
The purpose of the present paper is to investigate some inclusion properties of certain classes of analytic functions associated with a family of linear operators which are defined by means of the Hadamard product (or convolution). Some invariant properties under convolution are also considered for the classes presented here. The results presented here include several previous known results as their special cases.MSC:30C45.
Highlights
Let A denote the class of functions of the form ∞f (z) = z + akzk k=which are analytic in the open unit disk U = {z ∈ C : |z| < }
Which are analytic in the open unit disk U = {z ∈ C : |z| < }
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( ) = and |ω(z)| < for z ∈ U such that f (z) = g(ω(z))
Summary
Let N be a class of all functions φ which are analytic and univalent in U and for which φ(U) is convex with φ( ) = and Re{φ(z)} > for z ∈ U. Making use of the principle of subordination between analytic functions, many authors investigated the subclasses S*(η; φ), K(η; φ) and C(η, β; φ, ψ) of the class A for ≤ η, β < , φ, ψ ∈ N (cf [ ] and [ ]), which are defined by The operator Iλ(μ + , ) (λ > ; μ > – ) was introduced by Choi et al [ ] who investigated (among other things) several inclusion properties involving various subclasses of analytic and univalent functions.
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