Two dimensional divided differences revisited

The notion of two-dimensional divided difference was introduced by Academician T. Popoviciu, in 1934, for the case when the number of abscissas is equal to the number of coordinates. In his famous monograph, D. V. Ionescu recovered the Popoviciu’s definition and proved an integral representation for the two-dimensional divided difference of n-th order. In a recent monograph, M. Ivan introduced the notion of two-dimensional (m, n)-th order divided difference. The focus of the present paper is to establish some properties of the two dimensional divided difference of (m, n)-th order and to give a representation of the bivariate Lagrange interpolation polynomial in terms of above-divided differences.