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21/06/2014, 06:20
... all t1 < t2 in 0, and x ∈ a, 3a b /4 By 2.7 – 2.9 and using a similar method to that from Theorem 2.2, we can show that J is increasing on 0, and 2.6 holds This completes the proof The following ... functions I and J Theorem 2.5 Let f, g, I, and J be defined as above Then I t ≤ J t on 0, Proof By the identity a b /2 J t f tx 1−t 3a b a f t a b−x 1−t a 3b g 2x − a dx, 2.10 on 0, , 2.3 and using ... Proschan, and Y L Tong, Convex Functions, Partial Orderings, and Statistical Applications, c c vol 187 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1992 G.-S Yang and...