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Registry› Ma-Minda› Rational (Kumar–Ravichandran) starlike — φ(z) = 1 + z(k+z)/(k(k−z)), k=1+√2
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Rational (Kumar–Ravichandran) starlike — φ(z) = 1 + z(k+z)/(k(k−z)), k=1+√2

Ma-Minda

Canonical Key
ma_minda_rational_kr
Generating Definition
z f′(z)/f(z) ≺ φ(z) = 1 + z(k+z)/(k(k−z)), k=1+√2

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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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1
Instances
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Cited in papers
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12
In this φ-class

Facts (0)

Property Kind Params Holds Value / r Status Confidence

Verification Runs (0)

Verifier Property Direction Outcome Domain r Witness Engine

Instances (1)

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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.

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
“the S∗ R radius for the function F defined in (2.1)”
Radius of Starlikeness of Certain Analytic Functions high
Asha Sebastian, V. Ravichandran · 2021 · Mathematica Slovaca 71(1), 83-104
“S*_R = S*(ψ), ψ(z) = 1 + (z^2 k + z^2/(k^2 − kz)), k = √2 + 1 (rational function)”
Radius of starlikeness for some classes containing non-univalent functions high
Shalu Yadav, Kanika Sharma, V. Ravichandran · 2021
“the class S∗ R. (i) RS∗ R(T1)”
Starlikeness of Analytic Functions with Subordinate Ratios high
Rosihan M. Ali, Kanika Sharma, V. Ravichandran · 2021
“The following are the S∗ R-radius for the classes T1 and T2”
Bohr radius for certain classes of starlike and convex univalent functions high
Vasudevarao Allu, Himadri Halder · 2020
“φ(z) = 1+(z/k) ((k + z)/(k −z)), where k = √ 2 + 1. Then S∗(φ) reduces to the class S∗ R”
Radius of Starlikeness for Bloch Functions high
Somya Malik, V. Ravichandran · 2020
“Theorem 2.4. The S∗ R radius is the smallest positive root”
Starlikeness for Certain Close-to-Star Functions high
R. Kanaga, V. Ravichandran · 2020
“(vi) The radius RS∗ R (≈0.0481)”
Starlikeness of Certain Non-Univalent Functions high
Adam Lecko, V. Ravichandran, Asha Sebastian · 2020
“S*_R = S*(ψ), ψ(z) = 1 + (z^2 k + z^2/(k^2 − kz)), k = √2 + 1”
Coefficients of the Inverse Functions and Radius Estimates of Certain Starlike Functions high
Adiba Naz, Sushil Kumar, V. Ravichandran · 2019
“Class S*_R: f in A: zf'(z)/f(z) subordinate to phi_R(z) where phi_R(z) = 1 + z/k*(k+z)/(k-z)”
Mathematics & Statistics medium
Baskar Babujee Janani, V. Ravichandran, Nisha Bohra · 2025
“The sharp CVR radius for functions f such that f′ ∈ K(α, β)”
DIFFERENTIAL SUBORDINATION IMPLICATIONS FOR CERTAIN medium
Meghna Sharma, Sushil Kumar, Naveen Kumar Jain · 2024
“f ∈S∗ R if β ≥(3 + 2”
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