A critical investigation of various subclasses of functions whose real part is bounded

S K Bajpai

doi:10.1155/s0161171281000057

Abstract

In this paper we investigate various subclasses of univalent analytic functions. We find that many of the subclasses introduced in the recent years are no more new and infact coincide with the class due to Jakubowski. We further study the generalised Jakubowski class of univalent functions and obtain a representational formula and use it in deriving the coefficient relations for this class

Highlights

In this paper we investigate various subclasses of univalent analytic functions
Mogra and Juneja proposed that this class enables simple definition, and that thinking of this class helps in studying,other classes of starlike functions
Another class is investigated by Gopalakrishna nd Shetiya. They nned this class by SA(e,O,) and f E SA(u,O,D) if and only if f E S with eiAzf (z) isin cos I

Summary

Introduction

In this paper we investigate various subclasses of univalent analytic functions. We find that many of the subclasses introduced in the recent years are no more new and infact coincide with the class due to Jakubowski. Let M,m be arbitrary fixed real numbers satisfying the condition (re,M) E D* Dlt D2 and S*,M(’)m Jakubowski [7] introduced the class of regular functions f(z) akzk defined in E {z Iz[ < I} and satisfying the cndition eiUzf’(z) Mogra and Juneja ([9], [18], 7]) introduced a new class of Mogra and Juneja proposed that this class enables simple definition, and that thinking of this class helps in studying,other classes of starlike functions.

Results

Conclusion