Diamond Alpha Hilbert-Type Inequalities on Time Scales

Abstract

In this article, we will prove some new diamond alpha Hilbert-type dynamic inequalities on time scales which are defined as a linear combination of the nabla and delta integrals. These inequalities extend some known dynamic inequalities on time scales, and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proven by using some algebraic inequalities, diamond alpha Hölder inequality, and diamond alpha Jensen’s inequality on time scales.

Keywords

• Hilbert’s inequality
• dynamic inequality
• time scale
• diamond-α calculus