More on Hölder’s Inequality and It’s Reverse via the Diamond-Alpha Integral

Abstract

In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when T=R.

Keywords

• Hölder’s inequality
• generalization
• refinement
• diamond-<i>α</i> integral
• time scale