Symmetric Rogers-Hölder's inequalities on diamond-α calculus

Abstract

We present symmetric Rogers--Hö<span>lder's</span> inequalities on time scales when <span>$frac{1}{p}+frac{1}{q}+frac{1}{r}=0$</span> and <span>$frac{r}{p}+frac{r}{q}$</span> is not necessarily equal to <span>$1$</span> where <span>$p,$</span> <span>$q$</span> and <span>$r$</span> are <span>nonzero</span> real numbers.