Abstract
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
Highlights
Recent advances in the quantum B-splines, [4, 6, 17] have given us an opportunity to arise the question if there is a way to link quantum B-splines with a more general Peano kernel
Based on the q-Taylor Theorem, we introduce a more general form of the Peano kernel (q-Peano) which is applicable to non-di¤erentiable functions
We show that quantum B-splines are the q-Peano kernels of divided di¤erences
Summary
Recent advances in the quantum B-splines, [4, 6, 17] have given us an opportunity to arise the question if there is a way to link quantum B-splines with a more general Peano kernel. The quantum B-spline functions are piecewise polynomials whose quantum derivatives agree at the joins up to some order. Our objectives are to extend the Peano kernel and relate with the quantum B-splines. This extension is important because there are functions whose q-derivatives exist but whose classical derivatives fail to exist. The classical Peano kernel theorem provides a useful technique for computing the errors of approximations such as interpolation, quadrature rules and Bsplines. Quantum B-splines, Peano kernel, q-Taylor theorem, divided di¤erences, quantum derivatives, quantum integrals. Taking L(f ) as divided di¤erences we construct a relation between q-B-splines and q-Peano kernel. The error bounds of quadrature formula on the remainder involving q-integration is discussed
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
