A unifying approach to the difference operators and their applications

Résumé

In the present paper, we introduce the idea of difference operators $\Delta^\alpha$ and $\Delta^{(\alpha)} (\alpha\in\mathbb{R})$  and establish certain results which have several applications in Functional as well as Numerical analysis. Indeed, the operator $\Delta^\alpha$ generalizes several difference operators defined by K\i zmaz [1], Et [2], Et and \c{C}olak [3], Malkowsky and Parashar [4], Et [5], Malkowsky et al. [6], Baliarsingh [7] and many others (see [8-15]).