Abstract
We study a newly constructed subclass of bi-univalent functions.
Furthermore, we establish Chebyshev polynomial bounds for the coefficients,
and Fekete-Szeg¨o inequality, for the class Sσ(µ, t).
Results & Lemmas (5)
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Theorem 2.1.
Theorem 2.1. Let f given by (1.1) be in the class Sσ (µ, t). Then |a2| ≤ 4µt √ 2t p 4 (µ2 −µ) t2 + (µ + 1)2 and |a3| ≤16µ2t2 (µ + 1)2 + 2µt…
Theorem 2.1. Let f given by (1.1) be in the class Sσ (µ, t) . Then |a2| ≤ 4µt √ 2t p 4 (µ2 −µ) t2 + (µ + 1)2 and |a3| ≤16µ2t2 (µ + 1)2 + 2µt µ + 1.
Corollary 2.2.
Corollary 2.2. Let f given by (1.1) be in the class Sσ (t). Then |a2| ≤2t √ 2t and |a3| ≤4t2 + t.
Corollary 2.2. Let f given by (1.1) be in the class Sσ (t) . Then |a2| ≤2t √ 2t and |a3| ≤4t2 + t.
Theorem 3.1.
Theorem 3.1. Let f given by (1.1) be in the class Sσ (µ, t) and η ∈R. Then a3 −ηa2 2 ≤
Theorem 3.1. Let f given by (1.1) be in the class Sσ (µ, t) and η ∈R. Then a3 −ηa2 2 ≤
Corollary 3.2.
Corollary 3.2. If f ∈Sσ (µ, t), then a3 −a2 2 ≤ 2µt 1 + µ.
Corollary 3.2. If f ∈Sσ (µ, t) , then a3 −a2 2 ≤ 2µt 1 + µ.
Corollary 3.3.
Corollary 3.3. Let f given by (1.1) be in the class Sσ (t). Then a3 −a2 2 ≤t. Acknowledgement. The author thanks the referees for their…
Corollary 3.3. Let f given by (1.1) be in the class Sσ (t) . Then a3 −a2 2 ≤t. Acknowledgement. The author thanks the referees for their valuable sug- gestions to improve the paper. References 1. S¸. Altınkaya and S. Yal¸cın, Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces 2015 (2015), Article ID 145242 1-5. 2. S¸. Altınkaya and S. Yal¸cın, Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C.R. Acad
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