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- W2768072064 abstract "In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean $mathscr{M}$ the Kedlaya-type inequality $$ mathscr{A} bigl(x_{1},mathscr{M}(x_{1},x_{2}), ldots,mathscr{M}(x _{1},ldots,x_{n}) bigr) le mathscr{M} bigl( x_{1}, mathscr{A}(x _{1},x_{2}), ldots,mathscr{A}(x_{1},ldots,x_{n}) bigr) $$ holds for an arbitrary $(x_{n})$ ( $mathscr{A}$ stands for the arithmetic mean). We are going to prove the weighted counterpart of this inequality. More precisely, if $(x_{n})$ is a vector with corresponding (non-normalized) weights $(lambda_{n})$ and $mathscr{M}_{i=1}^{n}(x _{i},lambda_{i})$ denotes the weighted mean then, under analogous conditions on $mathscr{M}$ , the inequality holds for every $(x_{n})$ and $(lambda_{n})$ such that the sequence $(frac{lambda_{k}}{lambda_{1}+cdots+lambda_{k}})$ is decreasing." @default.
- W2768072064 created "2017-11-17" @default.
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- W2768072064 date "2018-04-25" @default.
- W2768072064 modified "2023-09-29" @default.
- W2768072064 title "On Kedlaya-type inequalities for weighted means" @default.
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- W2768072064 doi "https://doi.org/10.1186/s13660-018-1685-z" @default.
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