A characterization of weighted arithmetic means
J Aczél, C Wagner - SIAM Journal on Algebraic Discrete Methods, 1980 - SIAM
J Aczél, C Wagner
SIAM Journal on Algebraic Discrete Methods, 1980•SIAM… We prove, among other things, that theset of weighted arithmetic means is identical with the
set of functions f: R … We prove in this note that the k-allocation property assumed only for k 2
and k 3, characterizes weighted arithmetic means in the set of all averaging functions. In fact,
we obtain thefollowing more general result’ THEOREM. The function f:R -R satisfies the
k-allocation property for k 2 and k 3 and is continuous at a point or bounded from one side on
an (n-dimensional) interval or fust on a set of positive measure if and only if there exist real …
set of functions f: R … We prove in this note that the k-allocation property assumed only for k 2
and k 3, characterizes weighted arithmetic means in the set of all averaging functions. In fact,
we obtain thefollowing more general result’ THEOREM. The function f:R -R satisfies the
k-allocation property for k 2 and k 3 and is continuous at a point or bounded from one side on
an (n-dimensional) interval or fust on a set of positive measure if and only if there exist real …
We prove, among other things, that the set of weighted arithmetic means is identical with the set of functions satisfying (i) and (ii) for $k = 2,3:\sum _{i = 1}^k x_{ij} = s( j = 1,2, \cdots ,n ) \Rightarrow \sum _{i = 1}^k f( x_{i1} ,x_{i2} , \cdots ,x_{in} ) = s$.
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