Atıcı, Ferhan M.Yaldız, Hatice2020-04-302020-04-3020160008-43951496-4287https://doi.org/10.4153/CMB-2015-065-6https://hdl.handle.net/20.500.12684/3240WOS: 000376215100001In this paper, we introduce the definition of a convex real valued function f defined on the set of integers, Z. We prove that f is convex on Z if and only if Delta(2)f >= 0 on Z. As a first application of this new concept, we state and prove discrete Hermite-Hadamard inequality using the basics of discrete calculus (i.e., the calculus on Z). Second, we state and prove the discrete fractional Hermite-Hadamard inequality using the basics of discrete fractional calculus. We close the paper by defining the convexity of a real valued function on any time scale.en10.4153/CMB-2015-065-6info:eu-repo/semantics/closedAccessdiscrete calculusdiscrete fractional calculusconvex functionsdiscrete Hermite-Hadamard inequalityArticle592225233WOS:000376215100001Q2Q3