Radius of Starlikeness for Classes of Analytic Functions

Lee, See Keong; Khatter, Kanika; Ravichandran, V.

doi:10.1007/s40840-020-01028-0

Cited by 16 publications

(9 citation statements)

References 16 publications

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“…Further for Re g(z)/z > 0, the inequality |f (z)/g(z) − 1|< 1 was also discussed by Cho et al [5]. Likewise Khatter et al [15], Kumar et al [12] and Kumar [13] have also discussed similar expressions. Motivated by these classes, here below we define some subclasses of A n , where g ∈ A n ,…”

Section: Radius Problemsmentioning

confidence: 62%

On a subfamily of starlike functions related to Hyperbolic Cosine function

Mridula¹,

Kumar²

2022

Preprint

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Section: Radius Problemsmentioning

confidence: 62%

On a subfamily of starlike functions related to Hyperbolic Cosine function

Mridula¹,

Kumar²

2022

Preprint

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“…The radius of starlikeness of the class F χ 3 (see [23]) is (e) Let χ(z) = z + z 2 /2. If f ∈ F χ 1 , define functions q 1 , q 2 : D → C as q 1 (z) = f (z)/g(z) and q 2 (z) = g(z)/(z + z 2 /2).…”

Section: S *mentioning

confidence: 99%

Inclusion relations and radius problems for a subclass of starlike functions

Gupta,

Nagpal,

Ravichandran

2020

Preprint

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By considering the polynomial function φ car (z) = 1+z +z 2 /2, we define the class S * car consisting of normalized analytic functions f such that zf /f is subordinate to φ car in the unit disk. The inclusion relations and various radii constants associated with the class S * car and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.

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“…Thus, it is noted that R S * (S) is tanh π 4 ≈ 0.65579. Refer [5,9,16,20] for more literature on radius problems. For a fixed real number b in [0, 1], the class A b consists of analytic functions…”

Section: Introductionmentioning

confidence: 99%

Certain subclasses of Analytic Functions with Fixed Second Coefficient

Kumar¹,

Anand²,

Jain³

2022

Preprint

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This paper aims to pursue some classes of normalized analytic functions f with fixed second coefficient defined on open unit disk, such that (1 + z) 2 f (z)/z and (1 + z)f (z)/z are functions having positive real part. The radius of strongly starlikeness, the radius of lemniscate starlikeness, the radius of parabolic starlikeness and other starlikeness estimates are calculated for such functions. As well relevant connections of computed radii estimates with the existing one are also shown.

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Radius of Starlikeness for Classes of Analytic Functions

Cited by 16 publications

References 16 publications

On a subfamily of starlike functions related to Hyperbolic Cosine function

On a subfamily of starlike functions related to Hyperbolic Cosine function

Inclusion relations and radius problems for a subclass of starlike functions

Certain subclasses of Analytic Functions with Fixed Second Coefficient

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