Abstract
In this paper, we consider a strictly increasing continuous function beta, and we present a general quantum difference operator D-beta which is defined to be D(beta)f (t) = (f(beta(t)) -f(t))/(beta(t) - t). This operator yields the Hahn difference operator when beta(t) = qt + omega, the Jackson q-difference operator when beta(t) = qt, q is an element of (0, 1), omega > 0 are fixed real numbers and the forward difference operator when beta(t) = t + omega, omega > 0. A calculus based on the operator D-beta and its inverse is established.