Inequalities generated by chains of Jensen inequalities for convex functions

[摘要] References(8)In this paper, we study the monotonicity of some weighted differences between any two terms in chains of Jensen's inequalities for convex functions. The problem is reduced to the solvability of some weight equations or weight inequalities. Our proofs are based on the classical Jensen's inequality and some elementary identity involved combinatorial numbers.

[学科分类] 数学（综合）

[关键词] Convex function;Jensen's inequality;weighted difference;monotonicity;combinatorial identity