Starlike functions associated with a cardioid

By K. Sharma, N. Jain, V. Ravichandran. 2016

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Starlike and Convex Functions Associated with a Nephroid Domain (2019, unknown): “[28] introduced and investigated the class S∗ C := S∗(1 + 4z/3 + 2z/3) associated with the cardioid (9u + 9v − 18u+ 5) − 16(9u + 9v − 6u + 1) = 0, a heart-shaped curve.”
A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain (2019, background): “and also by the Alexandar-type relation, the authors in [11] defined the family Ccar by: Ccar = { f ∈ A : z f ′ (z) ∈ S∗ C (z ∈ ∆) } ; (2) see also [12,13].”
Bohr radius for certain classes of starlike and convex univalent functions (2020, background): “When φ(z) = 1+4z/3+2z(2)/3, the unit disk D is mapped onto a domain bounded by a cardiod and corresponding Ma-Minda starlike class S∗(φ) reduces to the class S∗ C (see [43]).”
Starlikness Associated with Cosine Hyperbolic Function (2020, unknown): “The function ∆(z) = 1 + (4)3 z + (2)3 z2 maps D into the image set bounded by the cardioid (y2 + x2 − 2x + 5 9 )2 − 16(y2 + x2 − 2 3 x + 1 9 ) = 0, which was examined in [9] and further studied in [10].”
Starlike Functions associated with a Petal Shaped Domain. (2020, methodology): “[19] studied the class S∗ C := S∗(1 + 4z/3 + 2z(2)/3) while the class S∗ s := S∗(1 + sin z) was examined by Cho et al.”