s-convex functions on discrete time domains

In the present work, we give the definition of an s-convex functions for a convex real-valued function f defined on the set of integers ℤ {Z} . We state and prove the discrete Hermite–Hadamard inequality for s-convex functions by using the basics of discrete calculus (i.e. the calculus on ℤ {Z} ). Finally, we state and prove the discrete fractional Hermite–Hadamard inequality for s-convex functions by using the basics of discrete fractional calculus.