New theorems on general integral inequalities, variants of the Levinson or Hardy integral inequality

This article makes contributions to the field of integral inequalities. Under certain assumptions, such as monotonicity and convexity, four theorems show how the Levinson or Hardy integral inequality can be generalized, improved or modified. Multiple functions are involved, and new lower and upper bounds are obtained. Applications are given, with an emphasis on inequalities using the Laplace transform of certain functions.