Preprint Article Version 1 This version is not peer-reviewed

Integral Representations for Bivariate Complex Geometric Mean and Applications

Version 1 : Received: 4 May 2017 / Approved: 4 May 2017 / Online: 4 May 2017 (08:44:25 CEST)

A peer-reviewed article of this Preprint also exists.

Feng Qi and Dongkyu Lim, Integral representations of bivariate complex geometric mean and their applications, Journal of Computational and Applied Mathematics 330 (2018), 41--58; Available online at https://doi.org/10.1016/j.cam.2017.08.005 Feng Qi and Dongkyu Lim, Integral representations of bivariate complex geometric mean and their applications, Journal of Computational and Applied Mathematics 330 (2018), 41--58; Available online at https://doi.org/10.1016/j.cam.2017.08.005

Journal reference: Journal of Computational and Applied Mathematics 2018, 330, 41-58
DOI: 10.1016/j.cam.2017.08.005

Abstract

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

Subject Areas

Lévy--Khintchine representation; integral representation; bivariate mean; bivariate complex geometric mean; reciprocal; Heronian mean; application

Readers' Comments and Ratings (4)

Comment 1
Received: 14 August 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first author of this paper.
Comment: Just now I received a good news: This preprint has been formally accepted for publishing in the Journal of Computational and Applied Mathematics in the year 2018.
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Response 1 to Comment 1
Received: 16 August 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first author of this paper.
Comment: Please cite this article as

Feng Qi and Dongkyu Lim, Integral representations of bivariate complex geometric mean and their applications, Journal of Computational and Applied Mathematics (2018), in press; Available online at http://dx.doi.org/10.1016/j.cam.2017.08.005.
Comment 2
Received: 20 September 2017
Commenter: Feng Qi (Click to see Publons profile: )
Commenter's Conflict of Interests: I am the first and corresponding author of this preprint
Comment: This preprint has been formally published as

Feng Qi and Dongkyu Lim, Integral representations of bivariate complex geometric mean and their applications, Journal of Computational and Applied Mathematics 330 (2018), 41--58; Available online at https://doi.org/10.1016/j.cam.2017.08.005
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Comment 3
Received: 20 September 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author of this preprint
Comment: Share your article [CAM_11257] published in Journal of Computational and Applied Mathematics

Article title: Integral representations of bivariate complex geometric mean and their applications
Article reference: CAM11257
Journal title: Journal of Computational and Applied Mathematics
Corresponding author: Dr. Dongkyu Lim
First author: Dr. Feng Qi
Final version published online: 06-Sep-2017
Full bibliographic details: Journal of Computational and Applied Mathematics 330C (2018) pp. 41-58
DOI information: 10.1016/j.cam.2017.08.005

Dear Dr. Qi,

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One can also find this information at https://qifeng618.wordpress.com/2017/09/07/share-your-article-cam_11257-published-in-journal-of-computational-and-applied-mathematics/
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