Univalency of weighted integral transforms of certain functions
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摘要
For β<1 and γ⩾0, let Pγ(β) denote the class of all normalized analytic functions f in the unit disc such thatReeiη(1-γ)f(z)z+γf′(z)-β>0,z∈Δ,for some η∈R. For f∈Pγ(β), we consider the integral transformVλ(f)(z)=∫01λ(t)f(tz)tdt,where λ(t) is a real-valued nonnegative weight function so that ∫01λ(t)dt=1. The main aim of this paper is to find conditions such that Vλ(f)∈P1(α) whenever f∈Pγ(β) for γ⩾1. We also obtain conditions such that Vλ(f)∈P1(β′) whenever f∈P0(β) for various choices of λ(t). As a useful consequence, we find conditions for certain hypergeometric functions to be univalent.
论文关键词:33C55,30C55,Subordination,Gaussian hypergeometric function,Univalent function,Starlike function,Convex function,Hadamard product
论文评审过程:Received 21 August 2003, Available online 15 August 2005.
论文官网地址:https://doi.org/10.1016/j.cam.2005.06.025