Remarks on interpolation in certain linear spaces (III)
Keywords:abstract interpolation polynomial, nonlinear mappings between normed spaces
AbstractIn this paper we study a way of extending the model of interpolating the real functions, with simple nodes, to the case of the functions defined between linear spaces, especially between linear normed spaces. In order to keep as many characteristics as possible from the case of the interpolation of real functions, in this paper we present a model of construction of the abstract interpolation polynomials, based on the properties of multilinear mappings. In this case we will define the divided differences and establish interpolation formulas with the rest expressed as a divided difference. We give the example of the type of interpolation polynomial built for non-linear mappings between spaces of functions defined on a certain interval.
How to Cite
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.