MathDB

1

Part of 1999 Poland - Second Round

Problems(1)

f(1/n) = (−1)^n, there are no increasing functions such f = g - h

Source: Polish second round 1999 p1

1/19/2020
Let f:(0,1)→Rf : (0,1) \to R be a function such that f(1/n)=(−1)nf(1/n) = (-1)^n for all n ∈ N. Prove that there are no increasing functions g,h:(0,1)→Rg,h : (0,1) \to R such that f=g−hf = g - h.
functionIncreasing functionalgebra