The Hermite-Hadamard inequality, which is related to convex functions, is a topic of frequent study in the mathematical community. Similarly, Mercer’s inequality, particularly in relation to Hermite- Hadamard and Jensen type inequalities, is also connected to convex functions and has recently been the focus of attention from researchers. In this study, new Hermite-Hadamard-Jensen-Mercer type integral inequalities for convex functions were obtained by employing the Power-mean and Ho¨lder inequalities, as well as their more general forms, namely the Improved Power-mean, Ho¨lder-I˙s¸can, and Young inequalities. Additionally, a comparison was conducted between the obtained results.