中文摘要：

证明了半序线性空间上线性泛函的两个Griiss型不等式,并由此给出了Karamata型积分不等式的一种推广形式,得到了一个新的Griiss型积分不等式及关于傅立叶系数的两个不等式.最后利用所得结论研究了关于矩阵及线性算子的一些Griiss型不等式.

英文摘要：

By proving two Griiss type inequalities for linear functional in partially ordered linear space,and then a generalization of the Karamata type integral inequality,a new Griiss type integral inequality is established and two inequalities on Fourier coefficients are given.As an appUcation,some Griiss type inequalities of matrices and linear operators are also studied.