Coefficient inequality for transforms of parabolic starlike and uniformly convex functions

D Vamshee Krishna,T Ramreddy,B Venkateswarlu

doi:10.5802/ambp.341

Abstract

Coefficient inequality for transforms of parabolic starlike and uniformly convex functions

Highlights

Let A denote the class of all functions f (z) of the form ∞f (z) = z + anzn n=2 (1.1)in the open unit disc E = {z : |z| < 1}
If F ≺ G and G(z) is univalent in the open unit disc E, the subordination is equivalent to F (0) = G(0) and range F (z) ⊆ range G(z)
For a univalent function in the class A, it is well known that the nth coefficient is bounded by n

Summary

Introduction

For a univalent function in the class A, it is well known that the nth coefficient is bounded by n. Several authors have investigated bounds for the Hankel determinant of functions belonging to various subclasses of univalent and multivalent functions [1, 12, 11].

Objectives

Results

Conclusion