论文标题
不变的手段，互补平均值以及β型的表征
Invariant means, complementary averages of means, and a characterization of the beta-type means
论文作者
论文摘要
我们证明，每当selfmapping $（m_1，\ dots，m_p）\ colon i^p \ to i^p $（（$ p \ in \ mathbb {n} $中，$ p \ in \ mathbb {n} $，$ m_i $ s as $ p $ variable是$ interval $ i $ y n in Interval and con的n $ i^$ i^p r^i^i^i^i^非空子集$ s \ subseteq \ {1，\ dots，p \} $存在一个独特确定的平均值$ k_s \ colon i^p \ to i $，以至于均值型映射$（n_1，\ d_p），n_p，n_p）\ colon i^p $ $ k $ i^p $ i^p $ i^$ i^$ i = k $ i = k $ i = k $ i; \在s $和$ n_i中：= m_i $否则。此外，\ begin {equination*} \ min（m_i \ colon i \ in S）\ le k_s \ le \ max（m_i \ colon i \ in S）。 \ end {equation*} 后来，我们使用此结果来：（1）构建一个$ k $ invariant均值型映射的广泛家族，（2）求解不变型型的功能方程，（3）（3）表征beta型含义。
We prove that whenever the selfmapping $(M_1,\dots,M_p)\colon I^p \to I^p$, ($p \in \mathbb{N}$ and $M_i$-s are $p$-variable means on the interval $I$) is invariant with respect to some continuous and strictly monotone mean $K \colon I^p \to I$ then for every nonempty subset $S \subseteq\{1,\dots,p\}$ there exists a uniquely determined mean $K_S \colon I^p \to I$ such that the mean-type mapping $(N_1,\dots,N_p) \colon I^p \to I^p$ is $K$-invariant, where $N_i:=K_S$ for $i \in S$ and $N_i:=M_i$ otherwise. Moreover \begin{equation*} \min(M_i\colon i \in S)\le K_S\le \max(M_i\colon i \in S). \end{equation*} Later we use this result to: (1) construct a broad family of $K$-invariant mean-type mappings, (2) solve functional equations of invariant-type, and (3) characterize Beta-type means.
