ISSN:
1573-8795
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let A denote the class of functions which are analytic in |z|〈1 and normalized so that f(0)=0 and f′(0)=1, and let R(α, β)⊂A be the class of functions f such thatRe[f′(z)+αzf″(z)]〉β,Re α〉0, β〈1. We determine conditions under which (i) f ∈ R(α1, β1), g ∈ R(α2, β2) implies that the convolution f×g of f and g is convex; (ii) f ∈ R(0, β1), g ∈ R(0, β2) implies that f×g is starlike; (iii) f≠A such that f′(z)[f(z)/z]μ-1 ≺ 1 + λz, μ〉0, 0〈λ〈1, is starlike, and (iv) f≠A such that f′(z)+αzf″(z) ≺ 1 + λz, α〉0, δ〉0, is convex or starlike. Bibliography: 16 titles.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02358538
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