Radius Problems for Starlike Functions Associated with the Sine Function

Majorization and Coefficient Problems for a General Class of Starlike Functions

“…so the following corollary concludes a majorization property for the subclass S * s := S * (1 + sin z) studied by Cho et al in [23] and also we have the result which was given by Tang et al in ([20], Theorem 2.1). (see [23]) and θ(z) = z 2 + z e z/2 , then we have θ(z) Θ(z) with ν(z) = 1 2+z . Therefore, from Corollary 3 we get…”

Logarithmic Coefficients for Univalent Functions Defined by Subordination

“…The following corollary concludes the logarithmic coefficients γ n for a subclass S * (1 + sin z) defined by Cho et al in [22], in which considering the proof of Theorem 1 and Corollary 1, the convexity radius for q 0 (z) = 1 + sin z is given by r 0 ≈ 0.345.…”

Starlike Functions Related to the Bell Numbers

“…In 2016, authors [7] determined the S * R -radius for various subclasses of starlike functions. For more results on radius problems, see [36][37][38][39][40][41].…”

“…Several authors considered various special cases of the class of Janowski starlike functions by considering some specific functions, namely ϕ q (z) := z + √ 1 + z 2 , ϕ 0 (z) := 1 + (z/k)((k + z)/(k − z)) (k = √ 2 + 1) , ϕ s (z) := 1 + sin z, and G α (z) := 1 + z/(1 − αz 2 ). Some of those classes are: S * L := S * ( √ 1 + z) [4], S * q := S * (ϕ q (z)) [5], S * e = S * (e z ) [6], S * R = S * (ϕ 0 ) [7], S * s = S * (ϕ s ) [8]) , BS * (α) := S * (G α (z)), 0 ≤ α < 1 [9,10]. For a brief survey on these classes, readers may refer to [11,12].…”