Article ID Journal Published Year Pages File Type
4643151 Journal of Computational and Applied Mathematics 2006 14 Pages PDF
Abstract
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.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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