Two reverse inequalities for Young's inequality were shown by M. Tominaga, using Specht ratio. In this short paper, we show alternative reverse inequalities for Young's inequality without using Specht ratio.

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Abstract. We give the tight bounds of Tsallis relative operator entropy by using Hermite-Hadamard's inequality. Some reverse inequalities related to Young's inequality are also given. In addition, operator inequalities for normalized positive linear map with Tsallis relative operator entropy are given.Mathematics subject classification (2010): 47A63, 46L05, 47A60.

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by the improvements of Young's inequality. We also give a generalized Han's inequality. MSC: 26D15; 94A17