Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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: 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.

Keywords

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

Subject

MATHEMATICS & COMPUTER SCIENCE, Analysis

Comments (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: (Click to see Publons profile: )
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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