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Canonical Key
ma_minda_cardioid_exp
Generating Definition
z f′(z)/f(z) ≺ φ(z) = 1 + z·e^z

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 (5)

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.

Trailokya Panigrahi, Eureka Pattnayak · 2025
“f(z) −f(−z) ≺1 + zez = p(z) (z ∈D), where the function p maps the unit disk D onto a cardioid domain”
S. Sivaprasad Kumar, Mridula Mundalia · 2023
“The S∗℘−radius is r4 = tanh2(π/2 √ 2e). (v) The S∗ρ−radius i”
Neha Verma, S. Sivaprasad Kumar · 2022
“Class S*_℘: f in A: zf'/f subordinate to 1 + z*e^z”
S. Sivaprasad Kumar, Kamaljeet Gangania · 2020
“zf'(z)/f(z) subordinate to 1 + z*exp(z) = wp(z); wp(D) is a cardioid domain”
Kamaljeet Gangania, S. Sivaprasad Kumar · 2020
“Lemma 1.1 ([29]) Let ℘(z) = 1 + zez.”
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