Our main target in this paper is to present some operator mean inequalities via operator monotone and operator monotone decreasing functions. In particular, with the help of these we generalize the Klamkin-McLenaghan inequality for every operator mean ${\sigma }_{\nu }$ where ${!}_{\nu }\le {\sigma }_{\nu }\le {\mathrm{\nabla }}_{\nu }$ and $0\le \nu \le 1$.

中文翻译：

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涉及算子单调函数的某些算子不等式

本文的主要目标是通过算子单调和算子单调递减函数给出算子平均不等式。尤其是，借助这些，我们针对每个算子平均值推广了Klamkin-McLenaghan不等式${\sigma }_{\nu }$ 哪里 ${！}_{\nu }\le {\sigma }_{\nu }\le {\mathrm{\nabla }}_{\nu }$ 和 $0\le \nu \le \mathrm{1个}$。