Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2018 / Cilt: 67 - Sayı: 2
A GENERALIZATION OF THE PEANO KERNEL AND ITS APPLICATIONS
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 229–241
- DOI
- —
Abstract
Based on the q-Taylor Theorem, we introduce a more general formof the Peano kernel (q-Peano) which is also applicable to non-di§erentiablefunctions. Then we show that quantum B-splines are the q-Peano kernels ofdivided di§erences. We also give applications to polynomial interpolation andconstruct examples in which classical remainder theory fails whereas q-Peanokernel works.