|
|||||
|
|
An integral representation for the weighted geometric mean and its applications |
|
| Authors: | Feng Qi Xiao Jing Zhang Wen Hui Li |
| Affiliation: | 1. School of Mathematics and Informatics, He’nan Polytechnic University, Jiaozuo, 454010, P. R. China 2. Luoyang, 471000, P. R. China 3. Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin, 300387, P. R. China |
| Abstract: | By virtue of Cauchy’s integral formula in the theory of complex functions, the authors establish an integral representation for the weighted geometric mean, apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function, and find a new proof of the well-known weighted arithmetic-geometric mean inequality. |
| Keywords: | Integral representation Cauchy's integral formula arithmetic mean geometric mean weighted arithmetic-geometric mean inequality complete Bernstein function new proof application |
| 本文献已被 CNKI 维普 SpringerLink 等数据库收录！ | |