Generalised Mean Averaging Interpolation by Discrete Cubic Splines

Abstract

The aim of this work is to introduce for a discrete function, certain discrete integrals which may reduce in particular to usual Riemann Stieltjes integrals. We name them as Discrete Stieltjes integrals. The existence and convergence of a discrete cubic interpolatory spline whose discrete Stieltjes integrals between consecutive meshpoints match with the corresponding integrals of a given periodic discrete function, are studied.