A study on reversed dynamic inequalities of Hilbert-type on time scales nabla calculus

Abstract

Abstract In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder’s inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N $\mathbb{T}=\mathbb{N}$ and T = R $\mathbb{T}=\mathbb{R}$ ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011).

Keywords

• Hilbert-type inequalities
• Time scales nabla calculus
• Hölder’s inequality