Abstract
Making use multiplier transformation and Ruscheweyh derivative,we introduce a new class of analytic functions RI(γ,λ,l,α,β) defined on the open unit disc, and investigate its various characteristics. Further we obtain distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity and neighborhood property for functions belonging to the class RI(γ,λ,l,α,β).MSC:30C45, 30A20, 34A40.
Highlights
Let A denote the class of functions of the form f (z) = z + ∞ j= ajzj, which are analytic and univalent in the open unit disc U = {z : z ∈ C : |z| < }
T is a subclass of A consisting of the functions of the form f (z) = z
For γ, λ, l ≥, ≤ α < and < β ≤, let RI(γ, λ, l, α, β) be the subclass of T consisting of functions that satisfying the inequality
Summary
(Ruscheweyh [ ]) For f ∈ A, n ∈ N, the operator Rn is defined by Rn : A → A,. [ , ] For f ∈ A, n ∈ N ∪ { }, λ, l ≥ , the operator I(n, λ, l)f (z) is defined by the following infinite series:. Following the work of Najafzadeh and Pezeshki [ ] we can define the class RI(γ , λ, l, α, β) as follows. For γ , λ, l ≥ , ≤ α < and < β ≤ , let RI(γ , λ, l, α, β) be the subclass of T consisting of functions that satisfying the inequality.
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