科研之友
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摘要
Under some natural assumptions on real functions f and g defined on a real interval I, we show that a two variable function M(f,g) : I(2) -> I defined by
M(f,g) (x,y) = (f + g)(-1) (f(x) + g(y))
is a generalization of the quasi-arithmetic mean. Necessary and sufficient conditions for: symmetry, quasi-arithmeticity, weighted quasi-arithmeticity, homogeneity of M(f,g), as well as equality of two such means are presented.
- 出版日期2010-6
