Abstract
We define a new general integral operator using Al-Oboudi differential operator. Also we introduce new subclasses of analytic functions. Our results generalize the results of Breaz, Guney, and Salagean.
Highlights
Let A denote the class of functions of the form ∞fz z anzn n2 which are analytic in the open unit disk U {z ∈ C : |z| < 1}, and S : {f ∈ A : f is univalent in U}.For f ∈ A, Al-Oboudi 1 introduced the following operator: D0f z f z, D1f z 1 − λ f z λzf z Dλf z, λ ≥ 0, Dkf z Dλ Dk−1f z, k ∈ N : {1, 2, 3, . . .} .Journal of Inequalities and ApplicationsIf f is given by 1.1, from 1.3 and 1.4 we see that Dkf z z1 n − 1 λ kanzn, k ∈ N0 : N ∪ {0}, n2 with Dkf 0 0.Remark 1.1
Fz z anzn n2 which are analytic in the open unit disk U {z ∈ C : |z| < 1}, and S : {f ∈ A : f is univalent in U}
A function f ∈ A is in the classes Sk δ, b, λ, where δ ∈ 0, 1, b ∈ C − {0}, λ ≥ 0, k ∈ N0, if and only if
Summary
Fz z anzn n2 which are analytic in the open unit disk U {z ∈ C : |z| < 1}, and S : {f ∈ A : f is univalent in U}. For f ∈ A, Al-Oboudi 1 introduced the following operator: D0f z f z , D1f z 1 − λ f z λzf z Dλf z , λ ≥ 0, Dkf z Dλ Dk−1f z , k ∈ N : {1, 2, 3, . . .}
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