Unveiling new reverse Hilbert-type dynamic inequalities within the framework of Delta calculus on time scales

Abstract

Some new reverse versions of Hilbert-type inequalities are studied in this paper. The results are established by applying the time scale versions of reverse Hölder's inequality, reverse Jensen's inequality, chain rule on time scales, and the mean inequality. As applications, some particular results (when $ \mathbb{T = N} $ and $ \mathbb{T = R} $) are considered. Our results provide some new estimates for these types of inequalities and improve some of those recently published in the literature.

Keywords

• hilbert-type inequalities
• reverse hilbert-type inequality
• delta calculus
• time scales