# Radius Problems for Functions Associated With a Nephroid Domain (Research Paper Sample)

This is my research paper based on nephroid Radius problems in geometric function theory.

In this work, we find sharp nephroid radii for several geometrically defined function classes introduced in the recent past. In particular, nephroid radii for the starlike classes are found to be 1/4. Moreover, radii problems related to the families defined in terms of ratio of functions are also discussed. Sharpness of certain radii estimates are illustrated graphically.

ORIGINAL PAPER

Radius problems for functions associated with a nephroid domain

Abstract

:= + −∈=−=S

Let N∗ e be the collection of all analytic functions f (z) defined on the open unit disk D and satisfying the normalizations f (0) f r(0) 1 0 such that the quantity zf r(z)/ f (z) assumes values from the range of the function ϕNe(z) 1 z z3/3, z D, which is the

interior of the nephroid given by

(u − 1)2

+ v2

4 3

— 9−

4v2

3 = 0.

SSIn this work, we find sharp SN∗ e-radii for several geometrically defined function classes introduced in the recent past. In particular, N∗ e -radius for the starlike class ∗ is found to be 1/4. Moreover, radii problems related to the families defined in terms of ratio of functions

are also discussed. Sharpness of certain radii estimates are illustrated graphically.

Keywords Starlike functions · Subordination · Radius problem · Bernoulli and Booth lemniscates · Cardioid · Nephroid

Mathematics Subject Classification 30C45 · 30C80

1 Introduction

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