We present a Bellman inequality involving operator means for

operators acting on a Hilbert space. We also give some Bellman

inequalities concerning sesquilinear forms. Finally, we refine the

Jensen's ...

In this paper we investigate a notion, related to $f$-divergence functional, of relative operator

entropy, which develops the theory started by J.I. Fujii and E.

Kamei [Math. Japonica 34 (1989), 341--348]. ...