Inclusion Relationships for Certain Subclasses of Meromorphic Functions Defined by Using the Extended Multiplier Transformations

Abstract EN

Let ∑ denote the class of analytic functions in the punctured unit disc U*={z:0<|z|<1}.

Set φλ,ℓm(z)=1/z+∑k=0∞[ℓ+λ(k+1)/ℓ]mzk (m∈ℕ0; ℓ>0; λ≥0; z∈U*), and define φλ,lm,μ in terms of the Hadamard product by φλ,lm(z)*φλ,lm,μ(z)=1/z(1-z)μ (μ>0;z∈U*).

In this paper, we introduce several new subclasses of analytic functions defined by means of the operator Iμm(λ,l)f(z)=φλ,lm,μ(z)*f(z) (f∈∑; m∈N0; l>0; λ≥0; μ>0). Inclusion properties of these classes and some applications involving integral operator are also considered.