论文标题
凸不平等及其应用于相对操作员熵
Convex inequalities and their applications to relative operator entropies
论文作者
论文摘要
不平等理论中的大量文献致力于研究詹森和扬的不平等。本文介绍了许多涉及对数符号函数和几何凸功能的新不平等。作为他们的后果，我们得出了Young不平等和Jensen不平等的改进。此外，还为有条件的两个功能开发了操作员Jensen的类型不等式。利用这些新的不平等现象，我们调查了与相对操作员熵有关的操作员不平等。
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex functions. As their consequences, we derive the refinements for Young's inequality and Jensen's inequality. In addition, the operator Jensen's type inequality is also developed for conditioned two functions. Utilizing these new inequalities, we investigate the operator inequalities related to the relative operator entropy.
