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a+b<=c+1, b+c<=a+1, c+a<=b+1 implies \sum a^2<=2abc+1

Source: Indian IMO Training Camp 2007-ST 2 P2

March 5, 2011
inequalitiesfunctioninequalities proposed

Problem Statement

Let a,b,ca,b,c be non-negative real numbers such that a+b≤c+1,b+c≤a+1a+b\leq c+1, b+c\leq a+1 and c+a≤b+1.c+a\leq b+1. Show that a2+b2+c2≤2abc+1.a^2+b^2+c^2\leq 2abc+1.
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