New Diamond-<i>α</i> Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces

Abstract

In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive σ-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.

Keywords

• time scales
• diamond-α integral
• measure spaces
• Steffensen-type inequality
• convex function