Properties of harmonic functions which are convex of order $ \bf \beta $ with respect to symmetric points

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Aini Janteng
Suzeini Abdul Halim

Abstract

Let $ \mathcal{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 $ \mathcal{D} $ and are related to the functions convex of order $ \beta(0\leq \beta <1) $, with respect to symmetric points. We obtain coefficient conditions, growth result, extreme points, convolution and convex combinations for the above harmonic functions.

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How to Cite
Janteng, A., & Halim, S. A. (2009). Properties of harmonic functions which are convex of order $ \bf \beta $ with respect to symmetric points. Tamkang Journal of Mathematics, 40(1), 31–39. https://doi.org/10.5556/j.tkjm.40.2009.34
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Papers
Author Biographies

Aini Janteng

School of Science and Technology, Universiti Malaysia Sabah, Locked Bag No.2073, 88999 Kota Kinabalu, Sabah, Malaysia.

Suzeini Abdul Halim

Institute of Mathematical Sciences, Universiti Malaya, 50603 Kuala Lumpur, Malaysia.

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