Abstract
Abstract By using the method of differential subordinations, we derive certain properties of meromorphically multivalent functions. 2010 Mathematics Subject Classification: 30C45; 30C55.
Highlights
Let Σ(p) denotes the class of meromorphically multivalent functions f(z) of the form ∞f (z) = z−p + ak−pzk−p k=1 p ∈ N = {1, 2, 3, . . .}, (1:1)which are analytic in the punctured unit diskU∗ = z : z ∈ C and 0 < |z| < 1 = U\ {0} .Let f(z) and g(z) be analytic in U
Which are analytic in the punctured unit disk
We say that f(z) is subordinate to g(z) in U, written f(z) ≺ g(z), if there exists an analytic function w(z) in U, such that |w(z)| ≤ |z| and f(z) = g(w(z)) (z Î U)
Summary
Let Σ(p) denotes the class of meromorphically multivalent functions f(z) of the form. Let f(z) and g(z) be analytic in U. We say that f(z) is subordinate to g(z) in U, written f(z) ≺ g(z), if there exists an analytic function w(z) in U, such that |w(z)| ≤ |z| and f(z) = g(w(z)) (z Î U). Several authors (see, e.g., [1-7]) considered some interesting properties of meromorphically multivalent functions. We aim at proving some subordination properties for the class Σ(p). Let h(z) be analytic and starlike univalent in U with h(0) = 0. Let p(z) be analytic and nonconstant in U with p(0) = 1. Our first result is contained in the following
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