By P. S. Bullen, D. S. Mitrinović, P. M. Vasić (auth.)

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**Extra resources for Means and Their Inequalities**

**Sample text**

Remark ( 10) It is easily seen that this inequality is strict unless a' and aare identical. Theorem 17. Proof.

3. 'nleorem 22. If'l U + and convex then Proof. 3. l !. 4I

N wi f (a i i .. l The case of equality is easily considered. ~ " by the induction hypothesis • CHAPTERI 24 Remarks (7). 189; the above proof is repeated in see also McShane [1), Pop [1). This important result will be referred to a J. It is equivalent to convexity, as is seen from the above proof. (9) As we will see J includes most classical inequalities as special cases although this may not always be obvious. Wn Wn ~ Thus if W is a positive n-tple wi m i l wi follows fram the concavity of log.