Some inequalities of Cauchy-Bunyakovsky-Schwarz type for sequences of bounded linear operators in Hilbert spaces and some applications are given.

Some new reverses of the Cauchy-Bunyakovsky-Schwarz inequality for n−tuples of real and complex numbers related to Cassels and Shisha-Mond results are given.

The results of the recent published paper by Masjed-Jamei et al. 2009 are extended to a larger class and some of subclasses are studied in the sequel. In other words, we generalize the well known Cauchy-Schwarz and Cauchy-Bunyakovsky inequalities having eight free parameters and then introduce some of their interesting subclasses.

Some generalizations of the well-known Cauchy-Schwarz inequality and the analogous Cauchy-Bunyakovsky inequality involving four free parameters are given for both discrete and continuous cases. Several particular cases of interest are also analyzed. Some of the applications of our main results include (for example) the Wagner inequality.

A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are given.

We prove an inequality for unitarily invariant norms that interpolates between the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality.