Results & Lemmas (6)
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Lemma 1.3
Lemma 1.3 see 13. If pz 1 c1z c2z2 c3z3 · · · is a function with positive real part in Δ, then for any complex number μ,…
Lemma 1.3 see 13. If pz 1 c1z c2z2 c3z3 · · · is a function with positive real part in Δ, then for any complex number μ, c2 −μc2 1 ≤2 max 1, |1 −2μ|. 1.8 2. Coefficient bounds By making use of Lemma 1.3, we prove the following bounds for the classes Σ∗φ and Σ∗ αφ.
Theorem 2.1.
Theorem 2.1. Let φz 1 B1z B2z2 · · ·. If fz given by 1.1 belongs to Σ∗φ, then for any complex number μ, i a1 −μa2 0 …
Theorem 2.1. Let φz 1 B1z B2z2 · · · . If fz given by 1.1 belongs to Σ∗φ, then for any complex number μ, i a1 −μa2 0 ≤ B1 2 max
Theorem 2.2.
Theorem 2.2. Let φz 1 B1z B2z2 · · ·. If fz given by 1.1 belongs to Σ∗ αφ, then for any complex number μ, i a1 −μa2 0…
Theorem 2.2. Let φz 1 B1z B2z2 · · · . If fz given by 1.1 belongs to Σ∗ αφ, then for any complex number μ, i a1 −μa2 0 ≤ B1 21 −2α max
Theorem 2.1
Theorem 2.1, we obtain the following results.
Theorem 2.1, we obtain the following results.
Theorem 3.3.
Theorem 3.3. Let φz 1 B1z B2z2 · · ·. If fz given by 1.1 belongs to Σ∗ λφ, then for any complex number μ, i a1 −μa2 0…
Theorem 3.3. Let φz 1 B1z B2z2 · · · . If fz given by 1.1 belongs to Σ∗ λφ, then for any complex number μ, i a1 −μa2 0 ≤ B1 λ 1λ 2 max
Theorem 3.4.
Theorem 3.4. Let φz 1 B1z B2z2 · · ·. If fz given by 1.1 belongs to Σ∗ α,λφ, then for any complex number μ, i a1 −μa2 0…
Theorem 3.4. Let φz 1 B1z B2z2 · · · . If fz given by 1.1 belongs to Σ∗ α,λφ, then for any complex number μ, i a1 −μa2 0 ≤ B1 1 −2αλ 1λ 2 × max 1,
Function classes studied:
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