Abstract
Making use of the operatorLυfor functions of the formfz=1/z+∑k=1∞akzk-1, which are analytic in the punctured unit discU∗={z:z∈Cand0<|z|<1}=U∖{0}, we introduce two subclasses of meromorphic functions and investigate convolution properties, coefficient estimates, and containment properties for these subclasses.
Highlights
Let Σ denote the class of meromorphic functions of the form f (z) = 1 z ∞ + ∑akzk−1, k=1 (1)which are analytic in the punctured unit disc U∗ = {z : z ∈ C and 0 < |z| < 1} = U \ {0}
For 0 ≤ λ < 1, −1 ≤ B < A ≤ 1, and b ∈ C∗ = C \ {0}, let ΣS∗λ[b; A, B] be the subclass of Σ consisting of function f(z) of the form (1) and satisfying the analytic criterion
Let ΣKλ[b; A, B] be the subclass of Σ consisting of function f(z) of the form (1) and satisfying the analytic criterion
Summary
Convolution Properties for Some Subclasses of Meromorphic Functions of Complex Order.
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