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Problem 1

Part of 2014 CIIM

Problems(1)

CIIM 2014 Problem 1

Source:

8/9/2016
Let g:[2013,2014]→Rg:[2013,2014]\to\mathbb{R} a function that satisfy the following two conditions:
i) g(2013)=g(2014)=0,g(2013)=g(2014) = 0, ii) for any a,b∈[2013,2014]a,b \in [2013,2014] it hold that g(a+b2)≤g(a)+g(b).g\left(\frac{a+b}{2}\right) \leq g(a) + g(b). Prove that gg has zeros in any open subinterval (c,d)⊂[2013,2014].(c,d) \subset[2013,2014].
CIIMCIIM 2014undergraduatefunction