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Cardioid starlike

Ma-Minda

Canonical Key
ma_minda_cardioid

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

0
Counterexamples
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4
Facts
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2
Verification runs
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1
Instances
0
Cited in papers
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14
In this φ-class

Facts (4)

Property Kind Params Holds Value / r Status Confidence
K membership {} ✓ 0.0653 🔬 screened numerical_strong
r* radius {} - r ≤ 0.700 🔬 screened numerical_strong
S* membership {} - 0.6363 retracted -
S membership {} ✗ - unscreened -

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 (14)

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.

Hankel determinants for starlike functions associated with a cardioid domain high
Mohsan Raza, Amina Riaz, and Paweł Zaprawa · 2025
“Theorem 1. Let f ∈S∗ car be given by (1.1).”
Radius Constants of Sigmoid Starlike Functions high
Priyanka Goel, S. Sivaprasad Kumar · 2022
“the classes S∗ RL, S∗ C and S∗ R”
Starlikeness of a product of starlike functions with non-vanishing polynomials high
Somya Malik, V. Ravichandran · 2022
“radius of starlikeness associated with a cardioid for the function F”
Radius of Starlikeness of Certain Analytic Functions high
Asha Sebastian, V. Ravichandran · 2021 · Mathematica Slovaca 71(1), 83-104
“S*_c = S*(1 + (4/3)z + (2/3)z^2) (cardioid)”
Radius of starlikeness for some classes containing non-univalent functions high
Shalu Yadav, Kanika Sharma, V. Ravichandran · 2021
“the class S∗ c . (i) RS∗c (T1) = 1/4 = 0.25”
Starlikeness of Analytic Functions with Subordinate Ratios high
Rosihan M. Ali, Kanika Sharma, V. Ravichandran · 2021
“S∗ C := S∗(ϕCAR), where ϕCAR(z) = 1 + 4z/3 + 2z2/3”
Bohr radius for certain classes of starlike and convex univalent functions high
Vasudevarao Allu, Himadri Halder · 2020
“For φ(z) = 1 + 4z/3 + 2z2/3, S∗(φ) reduces to S∗ C.”
Inclusion relations and radius problems for a subclass of starlike functions high
Prachi Gupta, Sumit Nagpal, V. Ravichandran · 2020
“Lemma 2.3. Let f ∈S∗ car and g ∈K. Then the function (f ∗g)(ρz)/ρ ∈S∗ car”
Radii problems for Ma-Minda Starlikeness high
Kamaljeet Gangania, S. Sivaprasad Kumar · 2020
“for ψ(z) = 1 + zez, z + √ 1 + z2, eez−1 and 1 + 4z/3 + 2z2/3”
Radius of Starlikeness for Bloch Functions high
Somya Malik, V. Ravichandran · 2020
“Theorem 2.2. The S∗ c -radius RS∗c ≈0.524423.”
Radius of Starlikeness for Classes of Analytic Functions high
Kanika Khatter, See Keong Lee, V. Ravichandran · 2020
“Ωc is the region bounded by the cardioid {x + iy : (9x2 + 9y2 −18x + 5)2”
Starlikeness of Certain Non-Univalent Functions high
Adam Lecko, V. Ravichandran, Asha Sebastian · 2020
“S*_c = S*(1 + (4/3)z + (2/3)z^2) (cardioid)”
Sufficient conditions for strong starlikeness high
Kanika Sharma, Nak Eun Cho, V. Ravichandran · 2020
“ϕCAR(z) := 1 + 4z 3 + 2z2 3 ≺1 + β”
Some Special Differential Subordinations high
Nisha Bohra, Sushil Kumar, V. Ravichandran · 2018
“then p(z) ≺φc(z) = 1 + 4z/3 + 2z2/3. Estimates on β are sharp.”
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