2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05Some mean-value theorems of the Cauchy type, which are connected with Jensen’s inequality, are given in [2] in discrete form and in [5] in integral form. Several further generalizations and applications of these results are presented here.
An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: are the vertices of triangles without obtuse inner angles such that has one side common with for .
Dato un sistema omogeneo di equazioni di convoluzione in spazi dotati di strutture analiticamente uniformi, si forniscono condizioni per ottenere teoremi di rappresentazione per le sue soluzioni.
We introduce and study the notion of Taylorian points of algebraic curves in , which enables us to define intrinsic Taylor interpolation polynomials on curves. These polynomials in turn lead to the construction of a well-behaved Hermitian scheme on curves, of which we give several examples. We show that such Hermitian schemes can be collected to obtain Hermitian bivariate polynomial interpolation schemes.