Sarikaya, Mehmet Zeki2025-03-242025-03-2420242147-625Xhttps://hdl.handle.net/20.500.12684/19547This paper aims to present a new refinement of the Jensen inequality specifically for convex functions. Building on this refinement, the paper derives various related inequalities, with a particular focus on Bullen's inequality and Ostrowski's inequality. Furthermore, it explores practical applications of these derived inequalities in the context of mean inequalities, providing a deeper understanding and broader utility of these mathematical concepts.eninfo:eu-repo/semantics/openAccessConvex function|Bullen inequality|Jensen inequality|Ostrowski inequality and Special meansArticle122112119