Majorization and Coefficient Problems for a General Class of Starlike Functions

Nak Eun Cho,Ali Ebadian,Ebrahim Analouei Adegani,Zahra Oroujy

doi:10.3390/sym12030476

Abstract

In the current paper, we study a majorization issue for a general category S * ( ϑ ) of starlike functions, the region of which is often symmetric with respect to the real axis. For various special symmetric functions ϑ , corresponding consequences of the main result are also presented with some relevant connections of the outcomes rendered here with those obtained in recent research. Moreover, coefficient bounds for some majorized functions are estimated.

Highlights

Let Φ represent the category of all analytic functions v in U that satisfy the requirements of v (0) = 0 and |v (z)| < 1 for z ∈ U, i.e., we consider Φ the set of Schwarz functions
Using the principle of subordination, a different subclass S ∗ (θ ) of starlike functions was defined by Ma and Minda [5] where θ is analytic and univalent with Re(θ (z)) > 0 in U, starlike with θ (0) = 1 and θ (U) is symmetric with respect to the real axis so that θ0 (0) > 0
Since θ (z) Θ(z), considering the concept of majorization, there is a function ν that is analytic in U with |ν(z)| ≤ 1 satisfying θ ( z ) = ν ( z ) Θ ( z )

Summary

Introduction

Using the principle of subordination, a different subclass S ∗ (θ ) of starlike functions was defined by Ma and Minda [5] where θ is analytic and univalent with Re(θ (z)) > 0 in U, starlike with θ (0) = 1 and θ (U) is symmetric with respect to the real axis so that θ0 (0) > 0. Coefficient estimates for majorized functions related to the class S ∗ (θ ) are obtained. Since θ (z) Θ(z), considering the concept of majorization, there is a function ν that is analytic in U with |ν(z)| ≤ 1 satisfying θ ( z ) = ν ( z ) Θ ( z ).

Results

Conclusion