# zbMATH — the first resource for mathematics

A generalization of the Peano kernel and its applications. (English) Zbl 1411.65027
Summary: Based on the $$q$$-Taylor Theorem, we introduce a more general form of the Peano kernel ($$q$$-Peano) which is also applicable to non-differentiable functions. Then we show that quantum B-splines are the $$q$$-Peano kernels of divided differences. We also give applications to polynomial interpolation and construct examples in which classical remainder theory fails whereas $$q$$-Peano kernel works.
##### MSC:
 65D07 Numerical computation using splines 41A05 Interpolation in approximation theory
Full Text: