Abstract
We define two new general integral operators for certain analytic functions in the unit disc and give some sufficient conditions for these integral operators on some subclasses of analytic functions.
Highlights
Let Ap(n) denote the class of all functions of the form ∞f (z) = zp + ∑ akzk (p, n ∈ N = {1, 2, . . .}) (1)k=p+n which is analytic in the open unit disc U = {z ∈ C : |z| < 1}
K=p+n which is analytic in the open unit disc U = {z ∈ C : |z| < 1}
By using the operator Dλm,l,α,p defined by (7), we introduce the new classes USmα,λp,l,n(δ, β, b) and UKmα,λp,l,n(δ, β, b) as follows
Summary
k=p+n which is analytic in the open unit disc U = {z ∈ C : |z| < 1}. In particular, we set Ap (1) := Ap, A1 (1) = A1 := A. where the function f is analytic in a simply connected region of the complex z-plane containing the origin, and the multiplicity of (z − ζ)−α is removed by requiring log(z − ζ) to be real when z − ζ > 0. (0 ≤ α < 1, k ∈ N) . α ≠ p + 1, p + 2, p + 3, . . . . Bulut [1] defined the general differential operator Dλm,l,α,p, namely, the generalization of the generalized Al-Oboudi differential operator as follows: D0f (z) = f (z) , Dλ1,,αl,pf (z) p Dλ2,,αl,pf (z) = Dλα,l,p (Dλ1,,αl,pf (z)) , Dλm,l,α,pf (z) = Dλα,l,p (Dλm,l−,p1,αf (z)) (m ∈ N) .
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