New Variations and Structural Refinements of Discrete Weighted Jensen and Hermite–Hadamard Inequalities Using ( α , m)‐Convex Mappings

This article develops new Hermite–Hadamard and Jensen‐type inequalities for the class of ( α , m)‐convex functions. New product forms of Hermite–Hadamard inequalities are established, covering multiple distinct scenarios. Several nontrivial examples and remarks illustrate the sharpness of these results and demonstrate how earlier inequalities can be recovered as special cases. In addition, we introduce three new variants of Jensen‐type inequalities, with their validity rigorously established via mathematical induction. These findings extend existing results and provide a broader framework for analyzing ( α , m)‐convex functions.