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]).
@article{19884,
title = {A unifying approach to the difference operators and their applications},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {31},
year = {2013},
doi = {10.5269/bspm.v33i1.19884},
language = {EN},
url = {http://dml.mathdoc.fr/item/19884}
}
Baliarsingh, Pinakadhar; Dutta, S. A unifying approach to the difference operators and their applications. Boletim da Sociedade Paranaense de Matemática, Tome 31 (2013) . doi : 10.5269/bspm.v33i1.19884. http://gdmltest.u-ga.fr/item/19884/