A Brunn-Minkowski-type inequality involving \(\gamma\)-mean variance and its applications
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Authors
Jiajin Wen
- College of Mathematics and Computer Science, Chengdu University, Chengdu, Sichuan 610106, P. R. China.
Shanhe Wu
- Department of Mathematics, Longyan University, Longyan, Fujian 364012, P. R. China.
Tianyong Han
- College of Mathematics and Computer Science, Chengdu University, Chengdu, Sichuan 610106, P. R. China.
Abstract
By means of the algebra, functional analysis, and inequality theories, we establish a Brunn-Minkowski-
type inequality involving
\(\gamma\)-mean variance:
\[\overline{var}^{[\gamma]} (f + g) \leq \overline{var}^{[\gamma]} f + \overline{var}^{[\gamma]} g; \quad \gamma \in [1; 2],\]
where \(\overline{var}^{[\gamma]} \varphi\) is the
\(\gamma\)-mean variance of the function
\(\varphi: \Omega\rightarrow (0,\infty)\) We also demonstrate the applications
of this inequality to the performance appraisal of education and business.
Share and Cite
ISRP Style
Jiajin Wen, Shanhe Wu, Tianyong Han, A Brunn-Minkowski-type inequality involving \(\gamma\)-mean variance and its applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 11, 5836--5849
AMA Style
Wen Jiajin, Wu Shanhe, Han Tianyong, A Brunn-Minkowski-type inequality involving \(\gamma\)-mean variance and its applications. J. Nonlinear Sci. Appl. (2016); 9(11):5836--5849
Chicago/Turabian Style
Wen, Jiajin, Wu, Shanhe, Han, Tianyong. "A Brunn-Minkowski-type inequality involving \(\gamma\)-mean variance and its applications." Journal of Nonlinear Sciences and Applications, 9, no. 11 (2016): 5836--5849
Keywords
- Brunn-Minkowski-type inequality
- \(\gamma\)-mean variance
- performance appraisal
- profit function
- allowance function.
MSC
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