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HERMITE-HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WITH A BOUNDED SECOND DERIVATIVE
HUAN-NAN SHI 장전수학회 2016 Proceedings of the Jangjeon mathematical society Vol.19 No.1
By applying results from the theory of majorization, some new inequalities of Hermite-Hadamard type for functions with a bounded second derivative are established.
Majorized proof of arithmetic-geometric-harmonic means inequality
HUAN-NAN SHI 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.4
As we all know, arithmetic -geometric mean inequalities are the most basic and important inequalities. To seek different method to prove them has been one of the study focuses and they have been proven by more than a hundred ways By using methods based on the theory of majorization, the arithmetic-geometric-harmonic means inequality is proved in a new way.
Schur convexity of Bonferroni means
DONGSHENG WANG,HUAN-NAN SHI 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.4
Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity of the Bonferroni means for n variables are investigated, and some mean value inequalities of n variables are established.
SCHUR CONVEXITY OF L-CONJUGATE MEANS AND ITS APPLICATIONS
Chun-Ru Fu,Huan-Nan Shi,Dong-Sheng Wang Korean Mathematical Society 2023 대한수학회지 Vol.60 No.3
In this paper, using the theory of majorization, we discuss the Schur m power convexity for L-conjugate means of n variables and the Schur convexity for weighted L-conjugate means of n variables. As applications, we get several inequalities of general mean satisfying Schur convexity, and a few comparative inequalities about n variables Gini mean are established.