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CHARACTERIZATIONS OF δ-ORDER ASSOCIATED WITH KANTOROVICH TYPE OPERATOR INEQUALITIES

In this note, we obtain more precise estimations than the constants are given in the paper by M.Fujii, E.Kamei and Y.Seo, Kantorovich type operator inequal- ities via grand Furuta inequality, Sci. Math., 3 (2000), 263-272. Among other, we show that the following statements are mutually equivalent for each δ ∈ (0,1): (i) K(m (p�δ)s n ,M (p�δ)s n ,n +1 ) 1 s A p ≥ B p