摘要：In this paper, we consider a strictly increasing continuous function β, and we present a general quantum difference operator D β $D_{\beta}$ which is defined to be D β f ( t ) = ( f ( β ( t ) ) − f ( t ) ) / ( β ( t ) − t ) ${D}_{\beta}f(t)= ({f(\beta(t))-f(t)} )/ ({\beta(t)-t} )$ . This operator yields the Hahn difference operator when β ( t ) = q t + ω $\beta(t)=qt+\omega$ , the Jackson q-difference operator when β ( t ) = q t $\beta (t)=qt$ , q ∈ ( 0 , 1 ) $q\in(0,1)$ , ω > 0 $\omega>0$ are fixed real numbers and the forward difference operator when β ( t ) = t + ω $\beta(t)=t+\omega$ , ω > 0 $\omega>($ . A calculus based on the operator D β $D_{\beta}$ and its inverse is established.
