New results concerning Chebyshev–Grüss-type inequalities via discrete oscillations

The classical form of Gruss' inequality was first published by G. Gruss and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. In the subsequent years, many variants of this inequality appeared in the literature. The aim of this paper is to consider some new bivariate Chebyshev-Gruss-type inequalities via discrete oscillations and to apply them to different tensor products of linear (not necessarily) positive, well-known operators. We also compare the new inequalities with some older results. In the end we give a Chebyshev-Gruss-type inequality with discrete oscillations for more than two functions.