• Corpus ID: 233004489

# Geometric properties of a domain with cusps

@inproceedings{Gandhi2021GeometricPO,
title={Geometric properties of a domain with cusps},
author={Shweta Gandhi and Prachi Gupta and S. Nagpal and Vaithiyanathan Ravichandran},
year={2021}
}
• Published 2 April 2021
• Mathematics
For n ≥ 4 (even), the function φnL(z) = 1 + nz/(n+ 1) + z/(n+ 1) maps the unit disk D onto a domain bounded by an epicycloid with n−1 cusps. In this paper, the class S∗ nL = S(φnL) is studied and various inclusion relations are established with other subclasses of starlike functions. The bounds on initial coefficients is also computed. Various radii problems are also solved for the class S∗ nL.

## References

SHOWING 1-10 OF 34 REFERENCES

### On a Subclass of Strongly Starlike Functions Associated with Exponential Function

Abstract. Let S ∗ e denote the class of analytic functions f in the open unit disk normalized by f (0) = f ′(0)−1= 0 and satisfying the condition z f′(z)/ f (z)≺ ez for |z| < 1. The structural

### Inclusion relations and radius problems for a subclass of starlike functions

• Mathematics
• 2020
By considering the polynomial function φcar(z) = 1+z+z /2, we define the class S∗ car consisting of normalized analytic functions f such that zf ′/f is subordinate to φcar in the unit disk. The

### Subclass of starlike functions associated with a limacon

• Mathematics
• 2018
Let S*LC represent a new subclass of analytic functions f defined in the open unit disk in the complex plane such that zf’(z)f(z) lies in the interior of the domain bounded by the limacon given by

### A subclass of starlike functions associated with left-half of the lemniscate of Bernoulli

• Mathematics
• 2014
Let $\mathcal{S}_{RL}^{*}$ denote the class of all analytic functions f in the open unit disk with the normalizations f(0) = f′(0) - 1 = 0 such that zf′(z)/f(z) lies in the interior of the left-half

### On the radius constants for classes of analytic functions

• Mathematics
• 2012
Radius constants for several classes of analytic functions on the unit disk are obtained. These include the radius of starlikeness of a positive order, radius of parabolic starlikeness, radius of

### Radius Problems for Starlike Functions Associated with the Sine Function

• Mathematics
Bulletin of the Iranian Mathematical Society
• 2018
Let $${\mathcal {S}}^*_s$$Ss∗ be the class of normalized analytic functions f defined on the unit disk such that the quantity $$zf'(z)/f(z)$$zf′(z)/f(z) lies in an eight-shaped region in the

### Starlike functions associated with exponential function and the lemniscate of Bernoulli

• Mathematics
• 2019
Let f be the function defined on the open unit disk, with $$f(0)=0=f'(0)-1$$f(0)=0=f′(0)-1, satisfying the subordinations $$zf'(z)/f(z)\prec \alpha + (1-\alpha )e^{z}$$zf′(z)/f(z)≺α+(1-α)ez or