Integral representations of bivariate complex geometric mean and their applications

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:330

Article

Qi, Feng^1,2  Lim, Dongkyu³ 

[1] Tianjin Polytech Univ, Dept Math, Coll Sci, Tianjin 300387, Peoples R China

[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China

[3] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

关键词: Integral representation;    Levy-Khintchine representation;    Bivariate complex geometric mean;    Multivariate geometric mean;    Weighted geometric mean;    Heronian mean;   

DOI  :  10.1016/j.cam.2017.08.005

来源: Elsevier

【 摘 要 】

In the paper, the authors survey integral representations (including the Levy-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. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free