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Duality for convolution on subclasses of analytic functions and weighted integral operators

Amini Ebrahim, Fardi Mojtaba, Al-Omari Shrideh, Nonlaopon Kamsing

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220168

In this article, we investigate a class of analytic functions defined on the unit open disc U = {z : ∣z∣ < 1}, such that for every f ∈ Pα(β , γ), α > 0, 0 ≤ β ≤ 1, 0 < γ ≤ 1, and ∣z∣ < 1, the inequality Re (…) > 0 holds. We find conditions on the numbers α, β, and γ such that Pα (β, γ) ⊆ SP (λ), for λ ∈ (…), where SP (λ) denotes the set of all λ-spirallike functions. We also make use of Ruscheweyh’s duality theory to derive conditions on the numbers α, β, γ and the real-valued function φ so that the integral operator Vφ(f) maps the set Pα(β, γ) into the set SP (λ), provided φ is non-negative normalized function (…) and (…).