NEW EXTENSION FOR REVERSE OF THE OPERATOR CHOI-DAVIS-JENSEN INEQUALITY

In this paper, we introduce the reverse of the operator Davis- Choi-Jensen’s inequality. Our results are employed to establish a new bound for the Furuta inequality. More precisely, we prove that, if A,B ∈ B (H) are self-adjoint operators with the spectra contained in the interval [m,M] with m < M and A ≤ B, then for any r ≥ 1 t > 1, t ∈ (0, 1) Ar ≤ ( M1H − A / M − m mrt + A − m1H M − m Mrt ) 1/t ≤ K (m,M, r)Br, where K (m,M, r) is the generalized Kantorovich constant. KCI Citation Count: 0