Estimating the defect in Jensen's Inequality
Estimating the defect in Jensen's Inequality
复制标题
估计 Jensen 不等式的缺陷
DOI：
10.5486/pmd.2006.3442
复制
发表时间：
2006
影响因子：
0.6
通讯作者：
A. M. Fink
中科院分区：
文献类型：
--
作者：
A. M. Fink
我们考虑Jensen不等式的两边可能有多大的差异。这与Grüss不平等有关。Grüss不等式给出了Chebyshev不等式中缺陷的估计，并在其他地方找到了一些应用，例如见[1]。这里我们考虑Jensen不等式中的缺陷。更准确地说，设所有积分都存在，μ是一个归一化度量，即∫b a dμ=1，则定义T(f，g)≡∫b
We consider how much the difference of the two sides of Jensen’s Inequality might be. It has a connection with Grüss Inequality. Grüss’ Inequality gives an estimate on the defect in the Chebyshev Inequality and has found some application elsewhere, see for example [1]. Here we consider the defect in Jensen’s Inequality. To be more precise, let all the integrals exist and μ be a normalized measure, i.e. ∫ b a dμ = 1. Then define T (f, g) ≡ ∫ b