Further Geometric Properties of a Subclass of Univalent Functions

Ezekiel A Oyekan

doi:10.14419/ijams.v7i1.30610

Abstract

This present paper aims to investigate further, certain characterization properties for a subclass of univalent function defined by a generalized differential operator. In particular, necessary and sufficient conditions for the function Â to belong to the subclass Â is established. Additionally, we provide the ð›…-neighborhood properties for the function Â by making use of the necessary and sufficient conditions. The results obtained are new geometric properties for the subclassÂ Â

Highlights

Let A denotes the class of functions f(z) which are analytic in the unit disk U = {z ∈ C: |z| < 1}
Let the class of all functions in A which are univalent in U be denoted by the symbol S and of the form f(z) = z + ∑∞k=2 anzn
It is well known that any function f ∊ S has the Taylor series expansion of the form (1), for details

Summary

Introduction

Let A denotes the class of functions f(z) which are analytic in the unit disk U = {z ∈ C: |z| < 1}. Let the class of all functions in A which are univalent in U be denoted by the symbol S and of the form f(z) = z + ∑∞k=2 anzn We denote by T the subclass of A consisting of functions f(z) ∊ A which are analytic and univalent in U and of the form f(z) = z − ∑∞k=2 ak zk, ak ≥ 0 (2) The class φμn(β, α), a subclass of univalent functions was introduced and studied by Oyekan [10].

Results

Conclusion