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functional equation with continous function

Source: tuymaada 2003

March 11, 2006
functionlimitreal analysisalgebrafunctional equation

Problem Statement

Find all continuous functions f(x)f(x) defined for all x>0x>0 such that for every xx, y>0y > 0 f(x+1x)+f(y+1y)=f(x+1y)+f(y+1x). f\left(x+{1\over x}\right)+f\left(y+{1\over y}\right)= f\left(x+{1\over y}\right)+f\left(y+{1\over x}\right) .
Proposed by F. Petrov
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