矩阵Fejér与Levin-Stečkin不等式
Matrix Fejér and Levin-Stečkin Inequalities
摘要：
Fe{j}ér和Levin-Stečkin不等式处理凸函数与对称函数的乘积的积分。本文的主要目标是提出这些不等式的可能的矩阵形式。特别地，对于凸函数和对数凸函数，给出了Fejér型优化结果.对于Levin-Stečkin型矩阵，我们给出了埃尔米特矩阵的部分Loewner序的更严格结果.
英文摘要：
Fe{j}ér and Levin-Stečkin inequalities treat integrals of the product of convex functions with symmetric functions. The main goal of this article is to present possible matrix versions of these inequalities. In particular, majorization results are shown of Fejér type for both convex and log-convex functions. For matrix Levin-Stečkin type, we present more rigorous results involving the partial Loewner ordering for Hermitian matrices.
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