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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We find conditions on the complex-valued function A : U → C defined in the unit disc U such that the differential inequality Re [A(z)p 2 (z) − α(zp 0 (z) − 1)2 + 2β(zp 0 (z))2 + γ] > 0 implies Re p(z) > 0, where p ∈ H[1, n], α, β ∈ C and n is a positive integer.
📌 3 Key Takeaways
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Objective & Hypothesis:We find conditions on the complex-valued function A : U → C defined in the unit disc U such that the differential inequality Re [A(z)p 2 (z) − α(zp 0 (z) − 1)2 + 2β(zp 0 (z))2 + γ] > 0 implies Re p(z) > 0, where p ∈ H[1, n], α, β ∈ C and n is a positive integer.
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Key Findings & Data:We find conditions on the complex-valued function A : U → C defined in the unit disc U such that the differential inequality Re [A(z)p 2 (z) − α(zp 0 (z) − 1)2 + 2β(zp 0 (z))2 + γ] > 0 implies Re p(z) > 0, where p ∈ H[1, n], α, β ∈ C and n is a positive integer.
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Conclusion & Impact:We find conditions on the complex-valued function A : U → C defined in the unit disc U such that the differential inequality Re [A(z)p 2 (z) − α(zp 0 (z) − 1)2 + 2β(zp 0 (z))2 + γ] > 0 implies Re p(z) > 0, where p ∈ H[1, n], α, β ∈ C and n is a positive integer.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Differential subordination · Dominant
Abstract
We find conditions on the complex-valued function A : U → C defined in the unit disc U such that the differential inequality Re [A(z)p 2 (z) − α(zp 0 (z) − 1)2 + 2β(zp 0 (z))2 + γ] > 0 implies Re p(z) > 0, where p ∈ H[1, n], α, β ∈ C and n is a positive integer.
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Cite This Article
Frasin, B. A. (2007). A NEW DIFFERENTIAL INEQUALITY. Hacettepe Journal of Mathematics and Statistics, Volume: 36 Issue: 1. https://ajindex.com/articles/1403787