1School of Mathematical Science, Chongqing Institute of Technology, Chongqing 400050, China. Email: wangliangcheng@163.com
2Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China. Email: xuzhang@amss.ac.cn
This paper is devoted to analyzing the monotonicity of some weighted differences between any two terms in a chain of Jensentype inequalities with repetitive sample. The problem is reduced to the solvability of some weight equations and/or weight inequalities. Complete characterization of the structure of solutions to the weight equations are also given.
Convex function, Jensentype inequality, repetitive sample, weighted difference, monotonicity, weight equation, weight inequality
