Geodesic
A Brunn-Minkowski-type inequality involving $\gamma$-mean variance and its applications
Wen, Jiajin1 ; Wu, Shanhe2 ; Han, Tianyong1
1 College of Mathematics and Computer Science, Chengdu University, Chengdu, Sichuan 610106, P. R. China
2 Department of Mathematics, Longyan University, Longyan, Fujian 364012, P. R. China
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 11, p. 5836-5849.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.009.11.12
Classification : 26D15, 26E60, 62J10
Keywords: Brunn-Minkowski-type inequality, \(\gamma\)-mean variance, performance appraisal, profit function, allowance function.

Wen, Jiajin 1 ; Wu, Shanhe 2 ; Han, Tianyong 1

1 College of Mathematics and Computer Science, Chengdu University, Chengdu, Sichuan 610106, P. R. China
2 Department of Mathematics, Longyan University, Longyan, Fujian 364012, P. R. China 
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Wen, Jiajin; Wu, Shanhe; Han, Tianyong. A Brunn-Minkowski-type inequality involving \(\gamma\)-mean variance and its applications. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 11, p. 5836-5849. doi : 10.22436/jnsa.009.11.12. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.11.12/

[1] Beckenbach, E. F.; Bellman, R. Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961

[2] Bjelica, M. Asymptotic planarity of Dresher mean values, Mat. Vesnik, Volume 57 (2005), pp. 61-63

[3] Gardner, R. J. The Brunn-Minkowski inequality, Bull. Amer. Math. Soc. (N.S.), Volume 39 (2002), pp. 355-405

[4] Gardner, R. J.; Vassallo, S. The Brunn-Minkowski inequality, Minkowski's first inequality, and their duals, J. Math. Anal. Appl., Volume 245 (2000), pp. 502-512

[5] Danskin, J. M. Dresher's inequality, Amer. Math. Monthly, Volume 59 (1952), pp. 687-688

[6] Dresher, M. Moment spaces and inequalities, Duke Math. J., Volume 20 (1953), pp. 261-271

[7] Gao, C. B.; Wen, J. J. Theory of surround system and associated inequalities, Comput. Math. Appl., Volume 63 (2012), pp. 1621-1640

[8] Han, T. Y.; Wu, S. H.; Wen, J. J. Sharp upper bound involving circuit layout system, J. Nonlinear Sci. Appl., Volume 9 (2016), pp. 1922-1935

[9] Hu, K. Some problems of analytic inequalities, (Chinese) Wuhan University Press, Wuhan, 2003

[10] Johnson, O. Information theory and the central limit theorem, Imperial College Press, London, 2004

[11] Nadarajah, S. A generalized normal distribution, J. Appl. Stat., Volume 32 (2005), pp. 685-694

[12] Páles, Z. Inequalities for sums of powers, J. Math. Anal. Appl., Volume 131 (1988), pp. 265-270

[13] Varanasi, M. K.; Aazhang, B. Parametric generalized Gaussian density estimation, J. Acoust. Soc. Am., Volume 86 (1989), pp. 1404-1415

[14] Wen, J. J.; Han, T. Y.; Cheng, S. S. Inequalities involving Dresher variance mean, J. Inequal. Appl., Volume 2013 (2013), pp. 1-29

[15] Wen, J. J.; Han, T. Y.; Gao, C. B. Convergence tests on constant Dirichlet series, Comput. Math. Appl., Volume 62 (2011), pp. 3472-3489

[16] Wen, J. J.; Huang, Y.; Cheng, S. S. Theory of \(\varphi\)-Jensen variance and its applications in higher education, J. Inequal. Appl., Volume 2015 (2015), pp. 1-40

[17] Wen, J. J.; Wu, S. H.; Gao, C. B. Sharp lower bounds involving circuit layout system, J. Inequal. Appl., Volume 2013 (2013), pp. 1-22

[18] Wen, J. J.; Wu, S. H.; Han, T. Y. Minkowski-type inequalities involving Hardy function and symmetric functions, J. Inequal. Appl., Volume 2014 (2014), pp. 1-17

[19] Wen, J. J.; Yan, J.; Wu, S. H. Isoperimetric inequalities in surround system and space science, J. Inequal. Appl., Volume 2016 (2016), pp. 1-28

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