Generalized Dynamic Inequalities of Copson Type on Time Scales

Abstract

This paper introduces novel generalizations of dynamic inequalities of Copson type within the framework of time scales delta calculus. The proposed generalizations leverage mathematical tools such as Hölder’s inequality, Minkowski’s inequality, the chain rule on time scales, and the properties of power rules on time scales. As special cases of our results, particularly when the time scale T equals the real line (T=R), we derive some classical continuous analogs of previous inequalities. Furthermore, when T corresponds to the set of natural numbers including zero (T=N0), the obtained results, to the best of the authors’ knowledge, represent innovative contributions to the field.