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Nephroid starlike

Ma-Minda

Canonical Key
ma_minda_nephroid

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
 →
4
Facts
 →
3
Verification runs
 →
1
Instances
0
Cited in papers
 →
14
In this φ-class

Facts (4)

Property Kind Params Holds Value / r Status Confidence
K membership {} ✗ -0.9510 unscreened -
r* radius {} - r ≤ 0.700 🔬 screened numerical_strong
S* membership {} - 0.5250 retracted -
S membership {} ✗ - unscreened -

Verification Runs (3)

Verifier Property Direction Outcome Domain r Witness Engine
boundary_scan_centered_v31 starlike disproves pass 0.950 0.99*exp(i*4.092661) boundary_v3.1
pointwise_starlike_iv starlike disproves pass 0.990 [-0.5819073997695485, -0.8009268244311979] gft-0.1.0-reaudit-20260610
boundary_scan_polynomial starlike disproves pass 0.950 0.99*exp(i*4.089593) 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.

On sharp third Hankel determinant for certain starlike functions high
Neha Verma, S. Sivaprasad Kumar · 2022
“If f ∈ S∗ Ne. Then |H3(1)| ≤ 32/81”
Radius Constants of Sigmoid Starlike Functions high
Priyanka Goel, S. Sivaprasad Kumar · 2022
“RS∗ SG(S∗ Ne) = rNe ≈ 0.43473”
Starlikeness of a product of starlike functions with non-vanishing polynomials high
Somya Malik, V. Ravichandran · 2022
“S∗ Ne = S∗(ϕNe) with ϕNe(z) = 1 + z −z3/3”
Coefficient Inequalities for certain Starlike and Convex functions high
Sushil Kumar KUMAR, Asena Çetınkaya · 2021
“is in the class S∗ Ne if and only if 1 z [ f(z) ∗z −Lz2”
Radius of starlikeness for some classes containing non-univalent functions high
Shalu Yadav, Kanika Sharma, V. Ravichandran · 2021
“the class S∗ Ne. (i) RS∗ Ne(T1) = 1/4 = 0.25”
Starlikeness of Analytic Functions with Subordinate Ratios high
Rosihan M. Ali, Kanika Sharma, V. Ravichandran · 2021
“The following are the S∗ Ne-radius for the classes T1 and T2”
Sufficiency for Nephroid Starlikeness using Hypergeometric Functions high
A. Swaminathan, Lateef Ahmad Wani · 2021
“Class S*_Ne: f in A with zf'(z)/f(z) subordinate to 1 + z - z^3/3”
Third Hankel Determinant Problem for Certain Subclasses of Analytic Functions Associated with Nephroid Domain high
Muhammad Ghaffar Khan, Bakhtiar Ahmad, Wali Khan Mashwani, Timilehin Gideon Shaba, Muhammad Arif · 2021
“Theorem 1. Let f ∈S∗ Ne of the form (1.1). Then |a2| ≤ 1, |a3| ≤ 1 2, |a4| ≤ 7 18”
Radius of Starlikeness for Bloch Functions high
Somya Malik, V. Ravichandran · 2020
“(3) The nephroid radius, RS∗”
Starlikeness of Certain Non-Univalent Functions high
Adam Lecko, V. Ravichandran, Asha Sebastian · 2020
“S*_Ne = S*(1 + z − z^3/3) (nephroid)”
Differential Subordinations for Starlike Functions Associated With A Nephroid Domain high
Lateef Ahmad Wani, A. Swaminathan · 2019
“ϕNe(z) := 1 + z −z3/3”
Radius Problems For Functions Associated with a Nephroid Domai high
Lateef Ahmad Wani, A. Swaminathan · 2019
“ΩNe := ϕNe(D), the region bounded by the nephroid (1.4)”
Starlike And Convex Functions Associated with A Nephroid domain having Cusps On The Real Axis high
Lateef Ahmad Wani, A. Swaminathan · 2019
“The function ϕNe(z) = 1 + z −z3/3 maps D onto the region bounded by the nephroid”
Radii of convexity associated with various subclasses of analytic functions for functions related to Kaplan classes medium
Baskar Babujee Janani, V. Ravichandran, Nisha Bohra · 2025
“The sharp CVNe radius for functions whose derivative belongs to K(α, β)”
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