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Classical starlike — φ(z) = (1+z)/(1−z)

Ma-Minda

Canonical Key
ma_minda_starlike
Generating Definition
z f′(z)/f(z) ≺ φ(z) = (1+z)/(1−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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Cited in papers
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14
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 (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.

An evolutionary approach to the coefficient problems in the class of starlike functions high
Piotr Jastrzȩbski, Adam Lecko · 2023
“THEOREM 5.1. If f ∈S∗”
On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application high
Rabha W. Ibrahim · 2020
“g ∈S∗( 1+ξ 1–ξ ) is starlike then”
Coefficients of the Inverse Functions and Radius Estimates of Certain Starlike Functions high
Adiba Naz, Sushil Kumar, V. Ravichandran · 2019
“A_2*A_4 - A_3^2 (inverse H_2(2) for S*) ≤ 3 for class S*”
New upper bounds of the third Hankel determinant for some classes of univalent functions high
Milutin Obradovic, Nikola Tuneski · 2019
“Class S*: f in A : z*f'(z)/f(z) subordinate to (1+z)/(1-z)”
Toeplitz determinants whose elements are the coefficients of univalent functions high
Md Firoz Ali, D. K. Thomas, A. Vasudevarao · 2017
“Theorem 2.2. Let f ∈ S∗be of the form (1.1). Then |T3(2)| ≤84”
An extremal problem for univalent functions high
Toshiyuki Sugawa, Li-Mei Wang · 2015
“Φ+(b, S∗) = +∞ and Φ−(b, S∗) = log(1 + b2) −log 4 −2b arctan b”
Fekete-Szegö problem for certain classes of Ma-Minda bi-univalent functions high
Halit Orhan, N. Magesh, V. K. Balaji · 2014
“phi0=(1+z)/(1-z)”
Starlike integral operators high
Sanford S. Miller and Petru T. Mocanu and Maxwell O. Reade · 2012
“feS*, then the function F(z) defined by (24) ... is again an element of S*”
On power deformations of univalent functions high
Yong Chan Kim, Toshiyuki Sugawa · 2011
“V (S∗) = {w : Re w > 0}”
Correspondence between spirallike functions and starlike functions high
Yong Chan Kim, Toshiyuki Sugawa · 2010
“a unique starlike func- tion g ∈S ∗in such a way”
Toeplitz Determinants in One and Higher Dimensions medium
Surya Giri, S. Sivaprasad Kumar · 2022
“Class S*: starlike functions, Re(zg'/g) > 0”
Pre-Schwarzian Norm Estimates for the class of Janowski Starlike Functions medium
Md Firoz Ali, Sanjit Pal · 2021
“Let f ∈ S∗ be of the form (1.1). Then the sharp inequality ||Tf|| ≤ 6”
Second Hankel determinant of logarithmic coefficients of certain analytic functions medium
Vasudevarao Allu, Vibhuti Arora · 2021
“Class S*: class of univalent starlike functions (α=0, β=0)”
On $H_3(1)$ Hankel determinant for some classes of univalent functions medium
K. O. Babalola · 2009
“Class S*: f in A with Re(zf'(z)/f(z)) > 0”
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