Jensen and Jensen-Mercer type inequalities for M(Ψ ,m)-convex functions

In this paper, we introduce a class of convexity known as \(M(Ψ ,m)\) -convexity. First, we investigate multi-term refinements of the inequality associated with \(M(Ψ ,m)\) -convexity. Then, our results are further enhanced and generalized through the application of weak sub-majorization theory. As applications, we derive novel refinements of the classical Hermite-Hadamard inequality for these notions. These findings expand upon and generalize recent work in the field, including the studies presented in [2, 19]. Our work contributes to the ongoing development of mathematical inequalities and their various applications.