Preprint Article Version 1 This version is not peer-reviewed

Lévy–Khintchine Representation of Toader–Qi Mean

Version 1 : Received: 15 March 2017 / Approved: 16 March 2017 / Online: 16 March 2017 (11:31:31 CET)

A peer-reviewed article of this Preprint also exists.

Qi, F.; Guo, B. Lévy-Khintchine Representation of Toader-Qi Mean. Mathematical Inequalities & Applications 2018, 21, 421-431. Qi, F.; Guo, B. Lévy-Khintchine Representation of Toader-Qi Mean. Mathematical Inequalities & Applications 2018, 21, 421-431.

Journal reference: Mathematical Inequalities & Applications 2018, 21, 421-431
DOI: https://doi.org/10.7153/mia-2018-21-29

Abstract

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

Subject Areas

Lévy–Khintchine representation; integral representation; Bernstein function; Stieltjes function; Toader–Qi mean; weighted geometric mean; Bessel function of the first kind; probabilistic interpretation; probabilistic interpretation; application in engineering; inequality

Readers' Comments and Ratings (3)

Comment 1
Received: 7 October 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author
Comment: This preprint has been accepted by the Mathematical Inequalities & Applications. Please cite this preprint as

Feng Qi and Bai-Ni Guo, LévyKhintchine representation of ToaderQi mean, Mathematical Inequalities & Applications 21 (2018), in press.
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Comment 2
Received: 7 October 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author
Comment: This preprint has been accepted by the Mathematical Inequalities & Applications. Please cite this preprint as

Feng Qi and Bai-Ni Guo, LévyKhintchine representation of ToaderQi mean, Mathematical Inequalities & Applications 21 (2018), in press.
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Comment 3
Received: 12 March 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author for this paper
Comment: Please cite this article as

Feng Qi and Bai-Ni Guo, Lévy–Khintchine representation of Toader–Qi mean, Mathematical Inequalities & Applications 21 (2018), no. 2, 421--431; Available online at https://doi.org/10.7153/mia-2018-21-29
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