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On Harmonic Functions Defined by Derivative Operator

Abstract

Let denote the class of functions that are harmonic univalent and sense-preserv- ing in the unit disk , where . In this paper, we introduce the class of functions which are harmonic in . A sufficient coefficient of this class is determined. It is shown that this coefficient bound is also necessary for the class if , where and . Coefficient conditions, such as distortion bounds, convolution conditions, convex combination, extreme points, and neighborhood for the class , are obtained.

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Correspondence to M. Darus.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Al-Shaqsi, K., Darus, M. On Harmonic Functions Defined by Derivative Operator. J Inequal Appl 2008, 263413 (2007). https://doi.org/10.1155/2008/263413

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Keywords

  • Harmonic Function
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  • Derivative Operator
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