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 operator inequality and use...

Regarding the generalizations of the Bessel inequality in Hilbert spaces

which are due to Bombieri and Boas–Bellman, we obtain a version of the

Bessel inequality and some generalizations of this inequality ...

We establish some operator versions of Bellman s inequality. In particular, we prove that if Phi: mathbb{B}( mathscr{H}) to mathbb{B}( mathscr{K}) is a unital positive linear map, A,B in mathbb{B}( mathscr{H})$ are ...