On Some New Hermite-Hadamard Type Inequalities for m-Convex Functions

Generalized convexity has emerged as an effective tool in the study of integral inequalities and has found applications across different areas of mathematical analysis. In this paper, we establish new Hermite–Hadamard type inequalities for m-convex functions through the use of Hölder inequality, the power-mean inequality, and related extensions. Moreover, we compare the derived inequalities to examine their relative strengths and establish the relationships among the obtained results. These novel inequalities presented in this research enhance the theoretical framework of Hermite-Hadamard type inequalities, offering greater accuracy, broader applicability, and a solid basis for future studies on m-convex functions.