Refined inequalities on the weighted logarithmic mean
Abstract
Inspired by the recent work by R.Pal et al., we give further refined inequalities for a convex Riemann integrable function, applying the standard Hermite-Hadamard inequality. Our approach is different from their one in PSMA2016. As corollaries, we give the refined inequalities on the weighted logarithmic mean and weighted identric mean. Some further extensions are also given.
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