Results & Lemmas (4)
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Theorem 1
Theorem 1 Let f(z) = z + ∞ P n=2 anzn be in the class G∗ Σ(α, x). Then |a2| ≤ |bx| p |bx| p |(3 −α) b2x2 −4 (px2b + qa)|, and |a3| ≤
Theorem 1 Let f(z) = z + ∞ P n=2 anzn be in the class G∗ Σ(α, x). Then |a2| ≤ |bx| p |bx| p |(3 −α) b2x2 −4 (px2b + qa)| , and |a3| ≤
Corollary 1
Corollary 1 Let f(z) = z + ∞ P n=2 anzn be in the class KΣ(x). Then |a2| ≤ |bx| p |bx| p |2b2x2 −4 (px2b + qa)|, and |a3| ≤|bx| 6
Corollary 1 Let f(z) = z + ∞ P n=2 anzn be in the class KΣ(x). Then |a2| ≤ |bx| p |bx| p |2b2x2 −4 (px2b + qa)| , and |a3| ≤|bx| 6
Corollary 2
Corollary 2 Let f(z) = z + ∞ P n=2 anzn be in the class HΣ(x). Then |a2| ≤ |bx| p |bx| p |3b2x2 −4 (px2b + qa)|, and |a3| ≤|bx| 3
Corollary 2 Let f(z) = z + ∞ P n=2 anzn be in the class HΣ(x). Then |a2| ≤ |bx| p |bx| p |3b2x2 −4 (px2b + qa)| , and |a3| ≤|bx| 3
Theorem 2
Theorem 2 Let f(z) = z + ∞ P n=2 anzn be in the class LΣ(x). Then |a2| ≤ |bx| p |bx| p |px2b + qa|, and |a3| ≤|bx| 4
Theorem 2 Let f(z) = z + ∞ P n=2 anzn be in the class LΣ(x). Then |a2| ≤ |bx| p |bx| p |px2b + qa| , and |a3| ≤|bx| 4
Function classes studied:
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