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Log-Convexity and Cauchy Means related to Berwald's Inequality

In this paper, we investigate the famous Berwald's inequality studying Berwald's difference in nonweighted and weighted case. We prove interesting property of log-convexity of this difference which allows us to deduce Lyapunov's type inequality for these differences. Cauchy type means in this setting are also studied.

Berwald's inequality; weighted Berwald's inequality; log-convexity; Cauchy means

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