Abstract
For β<1, let 𝒫γ(β) denote the class of all normalized analytic functions f in the unit disc Δ such that for some ϕ∈ℝ. Let 𝒮*(μ), 0≤μ<1, denote the usual class of starlike functions of order μ. Define 𝒦(μ)={f: zf′(z)∈𝒮*(μ)}, the class of all convex functions of order μ. In this paper, we consider integral transforms of the form The aim of this paper is to find conditions on λ (t) so that each of the transformations carries 𝒫γ(β) into 𝒮*(μ) or 𝒦(μ). A number of applications for certain special choices of λ (t) are also established. These results extend the previously known results by a number of authors.
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