Two Dimensional Divided Differences with Multiple Knots
نویسندگان
چکیده
The notion of two dimensional divided difference was introduced by T. Popoviciu in 1934. Many properties of these differences were obtained by D. V. Ionescu. Other properties of the mentioned differences were obtained by the authors of the present paper. The focus of the present paper is to establish properties of two dimensional differences in the case of multiple knots. First, we establish some properties of the univariate divided differences with multiple knots: a representation theorem using the determinants and a mean value theorem. Next, one proves the main results of the paper which are a representation theorem for the bivariate divided differences with multiple knots and a mean-value theorem for this kind of divided differences.
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