Examining New Convex Integral Inequalities

In this article, we introduce new convex integral inequalities based on a contemporary and adaptable analytical framework. These inequalities can handle composed functions, integral expressions, and ratio-type functionals, which make them applicable to a wide range of analysis problems. Our main result, in particular, complements a recent theorem from the literature by providing a valuable and non-trivial lower bound. The proofs are presented in full detail to ensure mathematical rigor, clarity, and reproducibility.