Sarikaya, Mehmet Zeki2026-07-012026-07-0120252645-8845https://doi.org/10.33401/fujma.1557116https://search.trdizin.gov.tr/tr/yayin/detay/1334975https://hdl.handle.net/20.500.12684/22854This 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.en10.33401/fujma.1557116info:eu-repo/semantics/openAccessMatematikArticle82657113349751557116