Abstract
Under some natural assumptions on real functions f and g defined on a real interval I, we show that a two variable function Mf,g : I2 → 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 Mf,g, as well as equality of two such means are presented.
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