English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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 $I$) isinvariant with respect to some continuous and strictly monotone mean $K \colonI^p \to I$ then for every nonempty subset $S \subseteq\{1,\dots,p\}$ thereexists a uniquely determined mean $K_S \colon I^p \to I$ such that themean-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 $K$-invariantmean-type mappings, (2) solve functional equations of invariant-type, and (3)characterize Beta-type means.

Invariant means, complementary averages of means, and a characterization of the beta-type means