... Lemma and the above argument □ (ii) Similarly Nakasuji et al Journal of Inequalities and Applications 2011, 2011:48 http://www.journalofinequalitiesandapplications.com/content/2011/1/48 Page of ... Tominaga, M: An estimate of Young type operator inequality and Specht ratio RIMS Kôkyûroku 1259, 173–178 (2002) (in Japanese) Hara, T, Uchiyama, M, Takahasi, S-E: A refinement of various mean inequalities ... Main results In this section, we first give a new interpretation of Jensen’s inequality by -mean Next, as an application, we consider some geometric properties of -means of a realvalued measurable...