Taylor theory associated with Hahn difference operator

Abstract In this paper, we establish Taylor theory based on Hahn’s difference operator $D_{q,\omega}$ Dq,ω which is defined by $D_{q,\omega}f(t)=\frac{f(qt+\omega)-f(t)}{t(q-1)+\omega}$ Dq,ωf(t)=f(qt+ω)−f(t)t(q−1)+ω , $t\neq\frac {\omega}{1-q}$ t≠ω1−q , where $q\in(0,1)$ q∈(0,1) and ω is a positive number.