Budakçi, Gülter; Oruç, Halil A generalization of the Peano kernel and its applications. (English) Zbl 1411.65027 Commun. Fac. Sci. Univ. Ank., Sér. A1, Math. Stat. 67, No. 2, 229-241 (2018). 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 Keywords:quantum B-splines; Peano kernel; \(q\)-Taylor theorem; divided differences; quantum derivatives; quantum integrals PDF BibTeX XML Cite \textit{G. Budakçi} and \textit{H. Oruç}, Commun. Fac. Sci. Univ. Ank., Sér. A1, Math. Stat. 67, No. 2, 229--241 (2018; Zbl 1411.65027) Full Text: DOI