N-dimension for dynamic generalized inequalities of Hölder and Minkowski type on diamond alpha time scales

Abstract

Expanding on our research, this paper introduced novel generalizations of H ölder's and Minkowski's dynamic inequalities on diamond alpha time scales. Specifically, as particular instances of our findings, we replicated the discrete inequalities established when $ \mathbb{T = N} $. Furthermore, our investigation extended to the continuous case with $ \mathbb{ T = R} $, revealing additional inequalities that are both new and valuable for readers seeking a comprehensive understanding of the topic.

Keywords

• hölder's inequality
• inequalities on time scales
• minkowski's inequality
• diamond alpha calculus