Abstract
In this paper, we introduce a new class of meromorphic multivalent functions in the puncturedunit discU*{z∈c:0 <|z|<1} . We obtain various resultsincluding coefficients inequality, convex set, radius of starlikeness and convexity, δ-neighborhoods , arithmetic mean and extreme points .
Highlights
Let Σp,αbe the class of functions of the form : 1 f z = zp+α + ∞ ak zk+p, ( p εN, α ≥ 0 ) (1)k=1−α are analytic and meromorphic multivalent in the punctured unit discU∗ = z ∈ C: 0 < z < 1 .Consider a subclass H* of the class Σp,α consisting functions of the form : ak zk+p, k=1−αThe convolution of two functions, f is given by (2) and ak ≥ 0, p εN 1 g z = zp+α + bk zk+p
Proof: Let f and g be the arbitrary elements of the classH(p, α, β, μ). for every e (0 ≤ e ≤ 1), we show that 1 − e f z + eg z ε H(p, α, β, μ)
Proof: We show that zF′ z F z + (p + α) ≤ (p + α) in z < R1
Summary
Let Σp,αbe the class of functions of the form : 1 f z = zp+α + Consider a subclass H* of the class Σp,α consisting functions of the form : 1 f z = zp+α + Let f ∈ H*be given by (2), theclass H(p,α, β, μ) is defined by 2-Coefficient Bounds: In the following theorem, we obtain the sufficient and necessary condition to be the function f in the class H(p,α, β, μ) .
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