Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities

Huan-Nan Shi; Shan-He Wu

doi:10.1186/s13660-017-1605-7

Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities

J Inequal Appl. 2018;2018(1):8. doi: 10.1186/s13660-017-1605-7. Epub 2018 Jan 8.

Authors

Huan-Nan Shi^{1

2}, Shan-He Wu¹

Affiliations

¹ 1Department of Mathematics, Longyan University, Longyan, Fujian 364012 P.R. China.
² 2Department of Electronic Information, Beijing Union University, Beijing, 100011 P.R. China.

Abstract

In this paper, we discuss the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the generalized geometric Bonferroni mean. Some inequalities related to the generalized geometric Bonferroni mean are established to illustrate the applications of the obtained results.

Keywords: Schur’s condition; geometric Bonferroni mean; inequality; majorization relationship.