New Diamond-alpha Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces

In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-alpha-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive sigma-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales T and differential calculus on R, we obtain already-known Steffensen-type inequalities.