- Research Article
- Open Access
Generalized Lazarevic's Inequality and Its Applications—Part II
© Ling Zhu. 2009
- Received: 21 July 2009
- Accepted: 30 November 2009
- Published: 24 December 2009
A generalized Lazarevic's inequality is established. The applications of this generalized Lazarevic's inequality give some new lower bounds for logarithmic mean.
- Lower Bound
- Concise Proof
Moreover, the inequality (1.1) can be extended as follows.
Let , then and . Let for we have that and is decreasing for so is decreasing for and is decreasing on by Lemma 2.2. Hence is decreasing on and is decreasing on by Lemma 2.1. Thus is decreasing on by Lemma 2.1.
Let , then . Let for we have that and is decreasing for so is decreasing for and is decreasing on by Lemma 2.2. Hence is increasing on and is decreasing on by Lemma 2.1. Thus is decreasing on by Lemma 2.1.
the proof of Theorem 1.3 is complete.
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