On Generalizations of Gruss Inequality in Inner Product Spaces and Applications

Abstract

Using a Kurepa's result for Gramians, we achieve refinements of well-known generalizations of Gruss inequality in inner product spaces. These results are further applied in L(2)(a, b) to derive improvements of some published trapezoid-Gruss and Ostrowki-Gruss type inequalities. Refinements of the discrete version of Gruss inequality as well as a reverse of the Schwarz inequality are also given.