Harmonic functions which are starlike of order β with respect to other points

Let H denote the class of functions f which are harmonic and univalent in the open unit disc D = {z : |z| < 1}. This paper defines and investigates a family of complex-valued harmonic functions that are orientation preserving and univalent in D and are related to the functions starlike of order β...

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Bibliographic Details
Main Authors: Aini Janteng, Suzeini Abdul Halim, Maslina Darus
Format: Article
Language:English
English
Published: Hikari Ltd 2008
Subjects:
Online Access:https://eprints.ums.edu.my/id/eprint/33611/2/Harmonic%20functions%20which%20are%20starlike%20of%20order%20%CE%B2%20with%20respect%20to%20other%20points.ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/33611/1/Harmonic%20Functions%20which%20are%20Starlike%20of%20Order%20%C3%9F%20with%20Respect%20to%20other%20Points.pdf
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Summary:Let H denote the class of functions f which are harmonic and univalent in the open unit disc D = {z : |z| < 1}. This paper defines and investigates a family of complex-valued harmonic functions that are orientation preserving and univalent in D and are related to the functions starlike of order β(0 ≤ β < 1), with respect to other points. We obtain growth result, extreme points, convolution and convex combinations for the above harmonic functions.