Some Properties of a Class of Harmonic Multivalent Functions Defined by an Integral Operator

Aqeel Ketab Al-Khafaji,Salwa Salman Abed,Waggas Galib Atshan

doi:10.29196/jubpas.v27i2.2129

Abstract

Some properties of a class of harmonic multivalent functions defined by an integral operator are introduced, like, coefficient estimates, distortion property, extreme points, inclusion results and closure under an integral operator for this class are obtained.

Highlights

Let and are real harmonic functions in the connected domain, the continuous functions, defined in is said to be harmonic in In any connected domain, we can write, where and are analytic in
+), consisting of all -valent harmonic functionsthat are sense-preserving in was defined by Ahuja and Jahangiri [3], where and are of the form
) we denote the class of harmonic multivalent functions of the form (1) such that where is defined by (2), Journal of University of Babylon for Pure and Applied Sciences (JUBAS) by University of Babylon is licened under a Creative Commons Attribution 4.0 International License. 2018

Summary

Introduction

Let and are real harmonic functions in the connected domain, the continuous functions, defined in is said to be harmonic in In any connected domain , we can write, where and are analytic in. Denote by the class of functions that are harmonic univalent and sense-preserving in the open unit disc * | | + where and are analytic in and is normalized by ( ) ( ) ( ) It may be worth nothing that, when the class ( ) was defined and studied by Jahangiri et al [4]. ( ) the class of analytic functions in . The modified Salagean integral operator [7] of given by (1) is defined as where

Results

Conclusion