MathDB

2

Part of 1994 Baltic Way

Problems(1)

Inequality involving 3 non-negative real numbers among 9

Source: Baltic Way 1994

12/22/2011
Let a1,a2,…,a9a_1,a_2,\ldots ,a_9 be any non-negative numbers such that a1=a9=0a_1=a_9=0 and at least one of the numbers is non-zero. Prove that for some ii, 2≤i≤82\le i\le 8, the inequality ai−1+ai+1<2aia_{i-1}+a_{i+1}<2a_i holds. Will the statement remain true if we change the number 22 in the last inequality to 1.91.9?
inequalitiestrigonometryalgebrapolynomialinequalities proposed