Geodesic
Homogeneous polynomials, root mean power, and geometric means in vector lattices
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 49-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that for a homogeneous orthogonally additive polynomial $P$ of degree $s\in\mathbb N$ from a uniformly complete vector lattice $E$ to some convex bornological space the equations $P(\mathfrak S_s(x_1,\ldots,x_N))= P(x_1)+\ldots+P(x_N)$ and $P(\mathfrak G(x_1,\ldots,x_s))=\check P(x_1,\ldots,x_s)$ hold for all positive $x_1,\ldots,x_s\in E$, where $\check P$ is an $s$-linear operator generating $P$, while $\mathfrak S_s(x_1,\ldots,x_N)$ and $\mathfrak G(x_1,\ldots,x_s)$ stand respectively for root mean power and geometric mean in the sense of homogeneous functional calculus. 
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     title = {Homogeneous polynomials, root mean power, and geometric means in vector lattices},
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Z. A. Kusraeva. Homogeneous polynomials, root mean power, and geometric means in vector lattices. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 49-53. http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a5/

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