On certain inequalities associated to curvature properties of the nonlinear PPH reconstruction operator

In this paper we study the curvature term for the Lagrange and PPH (Amat et al. in Found. Comput. Math. 6:193–225, 2006 and Ortiz and Trillo in Preprint, arXiv:1811.10566 , 2018 ) reconstruction operators in uniform and nonuniform meshes. We also make a comparison between both curvature terms in order to obtain an inequality which clearly shows that the PPH reconstruction presents a lower curvature term. Presenting a low curvature term is crucial in some applications, such as smoothing splines.