Abstract
In this paper, some integral inequalities based on the general quantum difference operator D-beta are deduced. Here, D-beta is defined by D(beta)f (t) = (f (beta(t))-f (t))/(beta(t)-t), where beta is a strictly increasing continuous function, defined on an interval IR, that has one fixed point s(0) is an element of I. The beta-Holder and beta-Minkowski inequalities are proved. Also, the beta-Gronwall, beta-Bernoulli, and some related inequalities are shown. Finally, the beta-Lyapunov inequality is established.