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Canonical Key
ma_minda_sigmoid

Image domain \(f(\mathbb{D})\)

The image of the unit disk under \(f\): concentric circles \(|z|=r\) and radial spokes mapped through \(f(z)=z+a_2z^2+\dots\); the bold curve is the boundary \(f(e^{i\theta})\). Rendered in your browser from the certified Taylor coefficients - nothing is computed server-side.

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Related

Facts (4)

Property Kind Params Holds Value / r Status Confidence
K membership {} ✓ 0.5995 🔬 screened numerical_strong
r* radius {} - r ≤ 0.700 🔬 screened numerical_strong
S* membership {} - 0.8155 retracted -
S membership {} ✓ - 🔬 screened numerical_strong

Verification Runs (2)

Verifier Property Direction Outcome Domain r Witness Engine
boundary_scan_centered_v31 starlike proves pass 0.999 - boundary_v3.1
boundary_scan_polynomial starlike proves pass 0.999 - boundary_v3.0

Instances (1)

{}

Papers in this φ-class (12)

Papers that explicitly study S*(φ) for this φ - conservatively tagged from the corpus (explicit φ formula, class symbol, or unambiguous name). Quote = the supporting passage.

Meghna Sharma, Sushil Kumar, Naveen Kumar Jain · 2024
“p(z) ≺φSG(z) := 2/(1 + e−z)”
Priyanka Goel, S. Sivaprasad Kumar · 2022
“The sharp S∗ SG,n-radius of the class S∗ n[A, B]”
Surya Giri, S. S. Kumar · 2022
“Class S*_SG: zf'/f subordinate to 2/(1+e^{-z})”
Somya Malik, V. Ravichandran · 2022
“the S∗ SG radius for the function F given in (2.1)”
Halit Orhan, G. Murugusundaramoorthy, Murat Çağlar · 2022
“Let h be a sigmoid function and (1.4) Φ(z) = 2h(z) = 1 + ∞ X”
Shalu Yadav, Kanika Sharma, V. Ravichandran · 2021
“the class S∗ SG. (i) RS∗ SG(T1)”
Adam Lecko, V. Ravichandran, Asha Sebastian · 2020
“S*_SG = S*(2/(1 + e^{−z})) (modified sigmoid)”
O.A. Fadipe-Joseph; N.A. Adeniran; B.B. Kadir; E.O. Adeniran · 2017
“Let h(z) be a sigmoid function and 𝜙(𝑧) = 2ℎ(𝑧) = 2 Definiti”
G. Murugusundaramoorthy, T. Janani · 2015
“Let h be a sigmoid function and Φ(z) = 2h(z)”
Baskar Babujee Janani, V. Ravichandran, Nisha Bohra · 2025
“The sharp CVSG radius for functions f such that f′ ∈ K(α, β)”
Musthafa Ibrahim, Bilal Khan, Lakhdar Ragoub, Ayman Alahmade · 2024
“Let g be a Sigmoid function defined in (1.2) and ϕ(z) = 2g(z)”
Nihad Hameed Shehab, Abdul Rahman S. Juma · 2021
“We symbolize to a sigmoid function and ( ) ( ) z e  1 2 ∑( ) || || ”
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