Results & Lemmas (2)
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Theorem 1.
Theorem 1. A function f belongs to the class Co(p) if and only if f satisfies (ii) and there exists a function ω holomorphic in D such that…
Theorem 1. A function f belongs to the class Co(p) if and only if f satisfies (ii) and there exists a function ω holomorphic in D such that ω(D) ⊂D and f ′′(z) f ′(z) = 2p 1 −zp + 2 p(1 −z/p) + 2zω(z) −α(1 + ω(z)) 1 −αz(1 + ω(z)) + z2ω(z), z ∈D, (7) where α :=
Theorem 2.
Theorem 2. Let f ∈Co(p), p ∈(0, 1) and n ∈ 2, 3, 4, 5. Then the domain of variability of an(f) is described by the inequality (6). A point…
Theorem 2. Let f ∈Co(p), p ∈(0, 1) and n ∈{2, 3, 4, 5}. Then the domain of variability of an(f) is described by the inequality (6). A point on the boundary of this domain is attained if and only if there exists a θ ∈[0, 2π) such that f = fθ, where fθ is defined as in (4).