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

• Main Authors: Aini Janteng, Suzeini Abdul Halim, Maslina Darus
• Format: Article
• Language: English; English
• Published: Hikari Ltd 2008
• Subjects: QA1-939 Mathematics
• 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; https://eprints.ums.edu.my/id/eprint/33611/; https://www.researchgate.net/profile/Suzeini-Abdul-Halim/publication/237751617_Harmonic_Functions_which_are_Starlike_of_Order_b_with_Respect_to_other_Points/links/00463532a584dc8c55000000/Harmonic-Functions-which-are-Starlike-of-Order-b-with-Respect-to-other-Points.pdf; https://doi.org/10.12988/ijcms
• Institution: Universiti Malaysia Sabah

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.