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 ∈ (0, 1) Ar ≤ (□□ m rt + □□ M rt )□ ≤ K (m, M, r)B r , where K (m, M, r) is the generalized Kantorovich constant.