On generalization of Mercer’s inequality involving averages of convex functions

Utilizing integral arithmetic mean and applying a generalized form of Niezgoda?s inequality, we present new proofs concerning the (m, n)-convexity of the integral arithmetic mean function, denoted as F. Additionally, we establish an inequality for divided differences by employing the extended form of Niezgoda?s inequality. Moreover, we demonstrate the convexity of the function defined by these divided differences.