College of Mathematics and Information Science, Henan Normal University

Abstract: As a generalization of grand Furuta inequality, recently Furuta obtain: If A≥ B≥0 with A>0, then for t∈[0,1] and p₁, p₂, p₃, p₄≥1, .... In this paper, we generalize this result for three operators as follow: If A≥B≥C≥0 with B>0, t∈[0,1] and p₁, p₂, ···, p_2n-1, p_2n≥1 for a natural number n. Then the following inequalities hold for r≥t, ..., where q_[2n]≡···. 

Key words: Furuta inequality, grand Furuta inequality, order preserving operator inequality