In this work, we give a multiple-term refinement of Young’s inequality which allow us to generalize and unify several results. As applications, we provide further refinements of a reversed AM–GM operator inequalities which extends and unifies two recent and important results due to Yang et al. (Math Slovaca 69:919–930, 2019) and Ren et al. (J Inequal Appl 2020:98, 2020) for positive linear maps and matrices. Also, our work deals with several other related results to both scalar and operator versions of the generalized Young’s inequality. In particular, we give a multiple-term refinement of Young’s inequalities for Hilbert–Schmidt norm, the determinants and the traces of positive definite matrices.

在这项工作中，我们对杨氏不等式进行了多次细化，使我们可以归纳和统一几个结果。作为应用，我们提供了反向AM-GM算子不等式的进一步改进，它扩大并统一了Yang等人最近的两个重要结果。（Math Slovaca 69：919-930，2019）和Ren等人。（J Inequal Appl 2020：98，2020）适用于正线性图和矩阵。此外，我们的工作还处理了广义扬氏不等式的标量和算子版本的其他几个相关结果。特别是，我们对希尔伯特-施密特范数，行列式和正定矩阵的迹线对杨氏不等式进行了多次细化。