Inclusion properties of certain subclasses of analytic functions defined by a multiplier transformation

Let A denote the class of analytic functions with the normalization ƒ (0) = ƒ′(0)-1 = 0 in the open unit disk U, set fλs(z)=z+∑k=2∞(k+λ1+λ)szk(s∈ℝ;λ>-1;z∈U)and define ƒλ,μs, in terms of the Hadamard productfλs(z)∗fλ,μs(z)=z(1−z)μ(μ>0;z∈U)In this paper, the authors introduce several new subclasses of analytic functions defined by means of the operator Iλ,μs : A → A, given byIλ,μsf(z)=fλ,μs(z)∗f(z)(f∈A;s∈ℝ;λ>-1;μ>0)Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.