Hardy-type inequalities play an important role in mathematical analysis and have been exten- sively studied due to their wide range of applications in inequality theory and related fields. In recent years, various convexity generalizations have been used as effective tools to obtain new integral inequalities and extend classical results. In this paper, we have obtained some new Hardy-type inequalities that general- ize certain known Hardy-type inequalities in the literature by utilizing different convexity classes, such as s−convex, quasi−convex, and η−convex functions, respectively. Also, our results reduce to previous work on classical convexity for specific choices of the parameters in the definitions of s−convexity and η−convexity.