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- W2994854392 abstract "Given two continuous functions $f,g:Itomathbb{R}$ such that $g$ is positive and $f/g$ is strictly monotone, a measurable space $(T,A)$, a measurable family of $d$-variable means $m: I^dtimes Tto I$, and a probability measure $mu$ on the measurable sets $A$, the $d$-variable mean $M_{f,g,m;mu}:I^dto I$ is defined by $$ M_{f,g,m;mu}(pmb{x}) :=left(frac{f}{g}right)^{-1}left( frac{int_T fbig(m(x_1,dots,x_d,t)big),dmu(t)} {int_T gbig(m(x_1,dots,x_d,t)big),dmu(t)}right) qquad(pmb{x}=(x_1,dots,x_d)in I^d). $$ The aim of this paper is to solve the equality and homogeneity problems of these means, i.e., to find conditions for the generating functions $(f,g)$ and $(h,k)$, for the family of means $m$, and for the measure $mu$ such that the equality $$ M_{f,g,m;mu}(pmb{x})=M_{h,k,m;mu}(pmb{x}) qquad(pmb{x}in I^d) $$ and the homogeneity property $$ M_{f,g,m;mu}(lambdapmb{x})=lambda M_{f,g,m;mu}(pmb{x}) qquad(lambda>0,,pmb{x},lambdapmb{x}in I^d), $$ respectively, be satisfied." @default.
- W2994854392 created "2019-12-26" @default.
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- W2994854392 date "2019-12-16" @default.
- W2994854392 modified "2023-09-26" @default.
- W2994854392 title "Equality and homogeneity of generalized integral means" @default.
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- W2994854392 doi "https://doi.org/10.1007/s10474-019-01012-6" @default.
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