Generalized Bullen Type Inequalities and Their Applications

This paper presents a novel extension of Bullen-type inequalities for convex functions by leveraging recently established generalized identities. Through rigorous proofs, we derive new inequalities that exhibit strong connections to both the left- and right-hand sides of the Hermite-Hadamard inequalities for Riemann-integrable functions. Additionally, we apply these results to various special means of two positive numbers.