科研之友
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摘要
We discuss the functional equation
f(M(x,y)) = f(N(x,y)) (x,y is an element of I)
where I is a nonvoid open subinterval of the set of real numbers a"e, f: I -> a"e is an unknown function, and M, N are weighted quasi-arithmetic means on I. Our typical assumption will be that M and N are comparable. Complete solution will be presented under the additional supposition that f is the product of the generating functions of M and N, respectively.
- 出版日期2013-1
