Unified Generalizations of Hardy-Type Inequalities Through the Nabla Framework on Time Scales

Abstract

This research investigates innovative extensions of Hardy-type inequalities through the use of nabla Hölder’s and nabla Jensen’s inequalities, combined with the nabla chain rule and the characteristics of convex and submultiplicative functions. We extend these inequalities within a cohesive framework that integrates elements of both continuous and discrete calculus. Furthermore, our study revisits specific integral inequalities from the existing literature, showcasing the wide-ranging relevance of our results.

Keywords

• Hardy’s inequality
• nabla Hölder’s inequality
• nabla Jensen’s inequality
• convexity
• continuous and discrete calculus
• time scales