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Canonical Key
ma_minda_crescent
Generating Definition
z f′(z)/f(z) ≺ φ(z) = z + √(1+z²)

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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Facts (0)

Property Kind Params Holds Value / r Status Confidence

Verification Runs (0)

Verifier Property Direction Outcome Domain r Witness Engine

Instances (1)

{}

Papers in this φ-class (8)

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.

Molla Basir Aahmed, Partha Pratim Roy · 2026
“Class S*$: f in S: zf'(z)/f(z) subordinate to z + sqrt(1+z^2); starlike functions associated with lune domain”
Bushra Kanwal, Arooj Iman, Shamsa Kanwal, Amal K. Alkhalifa · 2025
“If φ(z) = z + √ 1 + z2 was introduced by Raina and Sokol17, φ(z) maps U to the cres­ cent-shaped region”
Sanju Mandal, Molla Basir Ahamed · 2023
“zf'(z)/f(z) subordinate to z + sqrt(1+z^2)”
Asha Sebastian, V. Ravichandran · 2021 · Mathematica Slovaca 71(1), 83-104
“S*_$ = S*(z + √(1+z^2)) (lune)”
Kamaljeet Gangania, S. Sivaprasad Kumar · 2020
“for ψ(z) = 1 + zez, z + √ 1 + z2, eez−1 and 1 + 4z/3 + 2z2/3”
Adam Lecko, V. Ravichandran, Asha Sebastian · 2020
“S*_leftmoon = S*(z + √(1+z^2)) (lune)”
Virendra Kumar, R. B. Sharma · 2020
“function of the class 𝑆* (q) iff 𝑧𝑓′ (𝑧) 𝑓(𝑧) ≺ √ 1 + 𝑧2 + 𝑧”
Milutin Obradovic, Nikola Tuneski · 2019
“Class S*_q: f in A : z*f'(z)/f(z) subordinate to z+sqrt(1+z^2)”
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