Argument Properties for p-Valent Meromorphic Functions Defined by Differintegral Operator.

The integral operator Lmp (λ, ℓ)(λ, ℓ > 0; p ∈ N; m ∈ N0 = N ∪ {0}, where N = {1, 2, ...}) for functions of the form f(z) = z-p + P∞k=p+1 akzk which are analytic and p-valent in the punctured open unit disc U∗ = {z ∈ C : 0 < |z| < 1} = U\{0} was introduced by El-Ashwah [7]. The objective of the present paper is to extend the definition of the operator Lmp (λ, ℓ)f(z) for m ∈ Z = {0, ±1, ±2, ...} and drive interesting argument results of p-valent meromorphic functions defined by this differintegral operator. [ABSTRACT FROM AUTHOR]