New types of general single/multiple integral inequalities

Abstract

By introducing some concepts such as multiple integral inner product (MIIP) and multiple integral inner product space (MIIPS), new series of single/multiple integral inequalities are developed in a systematic way, which produce more accurate bounds on the cross terms from the direct Lyapunov method than those in the literature. Some previous integral inequalities including both single and multiple integral inequalities can be regarded as special cases of the proposed inequalities. Accordingly, such integral inequalities are less conservative in comparison with the existing integral inequalities.