Abstract
The paper aims to introduce a certain subclass S*g(A,B,α,p,j) of the class Σ*(p) of meromorphically multivalent functions with negative coefficients, defined by using the definitions of Hadamard product and subordination for two functions belong to the class Σ*(p). We first investigate the geometric characterization property, giving the coefficient estimates for functions in the class S*g(A,B,α,p,j). We also obtain the distortion theorem, radii of meromorphically p-valent starlikeness and convexity of order (0≤γ<p), neighborhood property, partial sums, convolution properties as well as integral operator and integral representation.
Highlights
Let Σ(p) denote the class of functions f(z) of the form: ∞ f ( z) = z−p + ∑a zn n p∈ N := {1, 2, 3...})
The aim intended to be achieved in the current analysis is to identify coefficient estimates, distortion theorem, radii of meromorphically p-valent star likeness and convexity of order (0≤γ
Depending on the earlier works by (Goodman, 1957; Ruscheweyh, 1981; Liu and Srivastava, 2004; Aouf, 2009; Aouf and El-Ashwah, 2009) that based upon the familiar concept of neighborhood of analytic functions, we introduce the definition of the δ-neighborhood of a function f (z)
Summary
Let Σ(p) denote the class of functions f(z) of the form: P − valent convex of orderγ inU * (r )}, The convolution or the Hadamard product of two meromorphic p-valent functions f and g, where f is given by (1.1) and A function f(z)∈ Σ*(p) is said to be in the class S*( A, B,α , p, j) if it satisfies the following g subordination condition: z (( f * ) )g (z) ( j+1)
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