A Brunn-Minkowski-type inequality involving \(\gamma\)-mean variance and its applications


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.


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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


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