Novel Hardy-Type Inequalities with Submultiplicative Functions on Time Scales Using Delta Calculus

Abstract

In this study, we apply Hölder’s inequality, Jensen’s inequality, chain rule and the properties of convex functions and submultiplicative functions to develop an innovative category of dynamic Hardy-type inequalities on time scales delta calculus. A time scale, denoted by T, is any closed nonempty subset of R. In time scale calculus, results are unified and extended. As particular cases of our findings (when T=R), we have the continuous analogues of inequalities established in some the literature. Furthermore, we can find other inequalities in different time scales, such as T=N, which, to the best of the authors’ knowledge, is a largely novel conclusion.

Keywords

• Hardy-type inequalities
• time scale delta calculus
• Hölder’s inequality
• Jensen’s inequality
• convex functions
• submultiplicative functions